title: Boolean algebra

text: The second diagram represents disjunction "x"∨"y" by shading those regions that lie inside either or both circles. The third diagram represents complement ¬"x" by shading the region "not" inside the circle.


title: Boolean algebra

text: While we have not shown the Venn diagrams for the constants 0 and 1, they are trivial, being respectively a white box and a dark box, neither one containing a circle. However we could put a circle for "x" in those boxes, in which case each would denote a function of one argument, "x", which returns the same value independently of "x", called a constant function. As far as their outputs are concerned, constants and constant functions are indistinguishable; the difference is that a constant takes no arguments, called a "zeroary" or "nullary" operation, while a constant function takes one argument, which it ignores, and is a "unary" operation.


title: Boolean algebra

text: Venn diagrams are helpful in visualizing laws. The commutativity laws for ∧ and ∨ can be seen from the symmetry of the diagrams: a binary operation that was not commutative would not have a symmetric diagram because interchanging "x" and "y" would have the effect of reflecting the diagram horizontally and any failure of commutativity would then appear as a failure of symmetry.


title: Boolean algebra

text: Idempotence of ∧ and ∨ can be visualized by sliding the two circles together and noting that the shaded area then becomes the whole circle, for both ∧ and ∨.


title: Boolean algebra

text: To see the first absorption law, "x"∧("x"∨"y") = "x", start with the diagram in the middle for "x"∨"y" and note that the portion of the shaded area in common with the "x" circle is the whole of the "x" circle. For the second absorption law, "x"∨("x"∧"y") = "x", start with the left diagram for "x"∧"y" and note that shading the whole of the "x" circle results in just the "x" circle being shaded, since the previous shading was inside the "x" circle.


title: Boolean algebra

text: The double negation law can be seen by complementing the shading in the third diagram for ¬"x", which shades the "x" circle.


title: Boolean algebra

text: To visualize the first De Morgan's law, (¬"x")∧(¬"y") = ¬("x"∨"y"), start with the middle diagram for "x"∨"y" and complement its shading so that only the region outside both circles is shaded, which is what the right hand side of the law describes. The result is the same as if we shaded that region which is both outside the "x" circle "and" outside the "y" circle, i.e. the conjunction of their exteriors, which is what the left hand side of the law describes.


title: Boolean algebra

text: The second De Morgan's law, (¬"x")∨(¬"y") = ¬("x"∧"y"), works the same way with the two diagrams interchanged.


title: Boolean algebra

text: The first complement law, "x"∧¬"x" = 0, says that the interior and exterior of the "x" circle have no overlap. The second complement law, "x"∨¬"x" = 1, says that everything is either inside or outside the "x" circle.


title: Boolean algebra

text: Digital logic is the application of the Boolean algebra of 0 and 1 to electronic hardware consisting of logic gates connected to form a circuit diagram. Each gate implements a Boolean operation, and is depicted schematically by a shape indicating the operation. The shapes associated with the gates for conjunction (AND-gates), disjunction (OR-gates), and complement (inverters) are as follows.


title: Boolean algebra

text: The lines on the left of each gate represent input wires or "ports". The value of the input is represented by a voltage on the lead. For so-called "active-high" logic, 0 is represented by a voltage close to zero or "ground", while 1 is represented by a voltage close to the supply voltage; active-low reverses this. The line on the right of each gate represents the output port, which normally follows the same voltage conventions as the input ports.


title: Boolean algebra

text: Complement is implemented with an inverter gate. The triangle denotes the operation that simply copies the input to the output; the small circle on the output denotes the actual inversion complementing the input. The convention of putting such a circle on any port means that the signal passing through this port is complemented on the way through, whether it is an input or output port.


title: Boolean algebra

text: The Duality Principle, or De Morgan's laws, can be understood as asserting that complementing all three ports of an AND gate converts it to an OR gate and vice versa, as shown in Figure 4 below. Complementing both ports of an inverter however leaves the operation unchanged.


title: Boolean algebra

text: More generally one may complement any of the eight subsets of the three ports of either an AND or OR gate. The resulting sixteen possibilities give rise to only eight Boolean operations, namely those with an odd number of 1's in their truth table. There are eight such because the "odd-bit-out" can be either 0 or 1 and can go in any of four positions in the truth table. There being sixteen binary Boolean operations, this must leave eight operations with an even number of 1's in their truth tables. Two of these are the constants 0 and 1 (as binary operations that ignore both their inputs); four are the operations that depend nontrivially on exactly one of their two inputs, namely "x", "y", ¬"x", and ¬"y"; and the remaining two are "x"⊕"y" (XOR) and its complement "x"≡"y".


title: Boolean algebra

text: The term "algebra" denotes both a subject, namely the subject of algebra, and an object, namely an algebraic structure. Whereas the foregoing has addressed the subject of Boolean algebra, this section deals with mathematical objects called Boolean algebras, defined in full generality as any model of the Boolean laws. We begin with a special case of the notion definable without reference to the laws, namely concrete Boolean algebras, and then give of the general notion.


title: Boolean algebra

text: A concrete Boolean algebra or field of sets is any nonempty set of subsets of a given set "X" closed under the set operations of union, intersection, and complement relative to "X".


title: Boolean algebra

text: Example 1. The power set 2 of "X", consisting of all subsets of "X". Here "X" may be any set: empty, finite, infinite, or even uncountable.


title: Boolean algebra

text: Example 2. The empty set and "X". This two-element algebra shows that a concrete Boolean algebra can be finite even when it consists of subsets of an infinite set. It can be seen that every field of subsets of "X" must contain the empty set and "X". Hence no smaller example is possible, other than the degenerate algebra obtained by taking "X" to be empty so as to make the empty set and "X" coincide.


title: Boolean algebra

text: Example 3. The set of finite and cofinite sets of integers, where a cofinite set is one omitting only finitely many integers. This is clearly closed under complement, and is closed under union because the union of a cofinite set with any set is cofinite, while the union of two finite sets is finite. Intersection behaves like union with "finite" and "cofinite" interchanged.


title: Boolean algebra

text: Example 4. For a less trivial example of the point made by Example 2, consider a Venn diagram formed by "n" closed curves partitioning the diagram into 2 regions, and let "X" be the (infinite) set of all points in the plane not on any curve but somewhere within the diagram. The interior of each region is thus an infinite subset of "X", and every point in "X" is in exactly one region. Then the set of all 2 possible unions of regions (including the empty set obtained as the union of the empty set of regions and "X" obtained as the union of all 2 regions) is closed under union, intersection, and complement relative to "X" and therefore forms a concrete Boolean algebra. Again we have finitely many subsets of an infinite set forming a concrete Boolean algebra, with Example 2 arising as the case "n" = 0 of no curves.


title: Boolean algebra

text: A subset "Y" of "X" can be identified with an indexed family of bits with index set "X", with the bit indexed by "x" ∈ "X" being 1 or 0 according to whether or not "x" ∈ "Y". (This is the so-called characteristic function notion of a subset.) For example, a 32-bit computer word consists of 32 bits indexed by the set {0,1,2...,31}, with 0 and 31 indexing the low and high order bits respectively. For a smaller example, if "X" = {"a,b,c"} where "a, b, c" are viewed as bit positions in that order from left to right, the eight subsets {}, {"c"}, {"b"}, {"b","c"}, {"a"}, {"a","c"}, {"a","b"}, and {"a","b","c"} of "X" can be identified with the respective bit vectors 000, 001, 010, 011, 100, 101, 110, and 111. Bit vectors indexed by the set of natural numbers are infinite sequences of bits, while those indexed by the reals in the unit interval [0,1] are packed too densely to be able to write conventionally but nonetheless form well-defined indexed families (imagine coloring every point of the interval [0,1] either black or white independently; the black points then form an arbitrary subset of [0,1]).


title: Boolean algebra

text: From this bit vector viewpoint, a concrete Boolean algebra can be defined equivalently as a nonempty set of bit vectors all of the same length (more generally, indexed by the same set) and closed under the bit vector operations of bitwise ∧, ∨, and ¬, as in 1010∧0110 = 0010, 1010∨0110 = 1110, and ¬1010 = 0101, the bit vector realizations of intersection, union, and complement respectively.


title: Boolean algebra

text: The set {0,1} and its Boolean operations as treated above can be understood as the special case of bit vectors of length one, which by the identification of bit vectors with subsets can also be understood as the two subsets of a one-element set. We call this the prototypical Boolean algebra, justified by the following observation.


title: Boolean algebra

text: This observation is easily proved as follows. Certainly any law satisfied by all concrete Boolean algebras is satisfied by the prototypical one since it is concrete. Conversely any law that fails for some concrete Boolean algebra must have failed at a particular bit position, in which case that position by itself furnishes a one-bit counterexample to that law. Nondegeneracy ensures the existence of at least one bit position because there is only one empty bit vector.


title: Boolean algebra

text: The final goal of the next section can be understood as eliminating "concrete" from the above observation. We shall however reach that goal via the surprisingly stronger observation that, up to isomorphism, all Boolean algebras are concrete.


title: Boolean algebra

text: The Boolean algebras we have seen so far have all been concrete, consisting of bit vectors or equivalently of subsets of some set. Such a Boolean algebra consists of a set and operations on that set which can be "shown" to satisfy the laws of Boolean algebra.


title: Boolean algebra

text: Instead of showing that the Boolean laws are satisfied, we can instead postulate a set "X", two binary operations on "X", and one unary operation, and "require" that those operations satisfy the laws of Boolean algebra. The elements of "X" need not be bit vectors or subsets but can be anything at all. This leads to the more general "abstract" definition.


title: Boolean algebra

text: For the purposes of this definition it is irrelevant how the operations came to satisfy the laws, whether by fiat or proof. All concrete Boolean algebras satisfy the laws (by proof rather than fiat), whence every concrete Boolean algebra is a Boolean algebra according to our definitions. This axiomatic definition of a Boolean algebra as a set and certain operations satisfying certain laws or axioms "by fiat" is entirely analogous to the abstract definitions of group, ring, field etc. characteristic of modern or abstract algebra.


title: Boolean algebra

text: Given any complete axiomatization of Boolean algebra, such as the axioms for a complemented distributive lattice, a sufficient condition for an algebraic structure of this kind to satisfy all the Boolean laws is that it satisfy just those axioms. The following is therefore an equivalent definition.


title: Boolean algebra

text: The section on axiomatization lists other axiomatizations, any of which can be made the basis of an equivalent definition.


title: Boolean algebra

text: Although every concrete Boolean algebra is a Boolean algebra, not every Boolean algebra need be concrete. Let "n" be a square-free positive integer, one not divisible by the square of an integer, for example 30 but not 12. The operations of greatest common divisor, least common multiple, and division into "n" (that is, ¬"x" = "n"/"x"), can be shown to satisfy all the Boolean laws when their arguments range over the positive divisors of "n". Hence those divisors form a Boolean algebra. These divisors are not subsets of a set, making the divisors of "n" a Boolean algebra that is not concrete according to our definitions.


title: Boolean algebra

text: However, if we "represent" each divisor of "n" by the set of its prime factors, we find that this nonconcrete Boolean algebra is isomorphic to the concrete Boolean algebra consisting of all sets of prime factors of "n", with union corresponding to least common multiple, intersection to greatest common divisor, and complement to division into "n". So this example while not technically concrete is at least "morally" concrete via this representation, called an isomorphism. This example is an instance of the following notion.


title: Boolean algebra

text: That is, up to isomorphism, abstract and concrete Boolean algebras are the same thing. This quite nontrivial result depends on the Boolean prime ideal theorem, a choice principle slightly weaker than the axiom of choice, and is treated in more detail in the article Stone's representation theorem for Boolean algebras. This strong relationship implies a weaker result strengthening the observation in the previous subsection to the following easy consequence of representability.


title: Boolean algebra

text: It is weaker in the sense that it does not of itself imply representability. Boolean algebras are special here, for example a relation algebra is a Boolean algebra with additional structure but it is not the case that every relation algebra is representable in the sense appropriate to relation algebras.


title: Boolean algebra

text: The above definition of an abstract Boolean algebra as a set and operations satisfying "the" Boolean laws raises the question, what are those laws? A simple-minded answer is "all Boolean laws", which can be defined as all equations that hold for the Boolean algebra of 0 and 1. Since there are infinitely many such laws this is not a terribly satisfactory answer in practice, leading to the next question: does it suffice to require only finitely many laws to hold?


title: Boolean algebra

text: In the case of Boolean algebras the answer is yes. In particular the finitely many equations we have listed above suffice. We say that Boolean algebra is finitely axiomatizable or finitely based.


title: Boolean algebra

text: Can this list be made shorter yet? Again the answer is yes. To begin with, some of the above laws are implied by some of the others. A sufficient subset of the above laws consists of the pairs of associativity, commutativity, and absorption laws, distributivity of ∧ over ∨ (or the other distributivity law—one suffices), and the two complement laws. In fact this is the traditional axiomatization of Boolean algebra as a complemented distributive lattice.


title: Boolean algebra

text: By introducing additional laws not listed above it becomes possible to shorten the list yet further; for instance, with the vertical bar representing the Sheffer stroke operation, the single axiom formula_7 is sufficient to completely axiomatize Boolean algebra. It is also possible to find longer single axioms using more conventional operations; see Minimal axioms for Boolean algebra.


title: Boolean algebra

text: Propositional logic is a logical system that is intimately connected to Boolean algebra. Many syntactic concepts of Boolean algebra carry over to propositional logic with only minor changes in notation and terminology, while the semantics of propositional logic are defined via Boolean algebras in a way that the tautologies (theorems) of propositional logic correspond to equational theorems of Boolean algebra.


title: Boolean algebra

text: Syntactically, every Boolean term corresponds to a propositional formula of propositional logic. In this translation between Boolean algebra and propositional logic, Boolean variables "x,y"... become propositional variables (or atoms) "P,Q"..., Boolean terms such as "x"∨"y" become propositional formulas "P"∨"Q", 0 becomes "false" or ⊥, and 1 becomes "true" or T. It is convenient when referring to generic propositions to use Greek letters Φ, Ψ... as metavariables (variables outside the language of propositional calculus, used when talking "about" propositional calculus) to denote propositions.


title: Boolean algebra

text: The semantics of propositional logic rely on truth assignments. The essential idea of a truth assignment is that the propositional variables are mapped to elements of a fixed Boolean algebra, and then the truth value of a propositional formula using these letters is the element of the Boolean algebra that is obtained by computing the value of the Boolean term corresponding to the formula. In classical semantics, only the two-element Boolean algebra is used, while in Boolean-valued semantics arbitrary Boolean algebras are considered. A tautology is a propositional formula that is assigned truth value "1" by every truth assignment of its propositional variables to an arbitrary Boolean algebra (or, equivalently, every truth assignment to the two element Boolean algebra).


title: Boolean algebra

text: These semantics permit a translation between tautologies of propositional logic and equational theorems of Boolean algebra. Every tautology Φ of propositional logic can be expressed as the Boolean equation Φ = 1, which will be a theorem of Boolean algebra. Conversely every theorem Φ = Ψ of Boolean algebra corresponds to the tautologies (Φ∨¬Ψ) ∧ (¬Φ∨Ψ) and (Φ∧Ψ) ∨ (¬Φ∧¬Ψ). If → is in the language these last tautologies can also be written as (Φ→Ψ) ∧ (Ψ→Φ), or as two separate theorems Φ→Ψ and Ψ→Φ; if ≡ is available then the single tautology Φ ≡ Ψ can be used.


title: Boolean algebra

text: One motivating application of propositional calculus is the analysis of propositions and deductive arguments in natural language. Whereas the proposition "if "x" = 3 then "x"+1 = 4" depends on the meanings of such symbols as + and 1, the proposition "if "x" = 3 then "x" = 3" does not; it is true merely by virtue of its structure, and remains true whether ""x" = 3" is replaced by ""x" = 4" or "the moon is made of green cheese." The generic or abstract form of this tautology is "if "P" then "P"", or in the language of Boolean algebra, ""P" → "P"".


title: Boolean algebra

text: Replacing "P" by "x" = 3 or any other proposition is called instantiation of "P" by that proposition. The result of instantiating "P" in an abstract proposition is called an instance of the proposition. Thus ""x" = 3 → "x" = 3" is a tautology by virtue of being an instance of the abstract tautology ""P" → "P"". All occurrences of the instantiated variable must be instantiated with the same proposition, to avoid such nonsense as "P" → "x" = 3 or "x" = 3 → "x" = 4.


title: Boolean algebra

text: Propositional calculus restricts attention to abstract propositions, those built up from propositional variables using Boolean operations. Instantiation is still possible within propositional calculus, but only by instantiating propositional variables by abstract propositions, such as instantiating "Q" by "Q"→"P" in "P"→("Q"→"P") to yield the instance "P"→(("Q"→"P")→"P").


title: Boolean algebra

text: An axiomatization of propositional calculus is a set of tautologies called axioms and one or more inference rules for producing new tautologies from old. A "proof" in an axiom system "A" is a finite nonempty sequence of propositions each of which is either an instance of an axiom of "A" or follows by some rule of "A" from propositions appearing earlier in the proof (thereby disallowing circular reasoning). The last proposition is the theorem proved by the proof. Every nonempty initial segment of a proof is itself a proof, whence every proposition in a proof is itself a theorem. An axiomatization is sound when every theorem is a tautology, and complete when every tautology is a theorem.


title: Boolean algebra

text: Propositional calculus is commonly organized as a Hilbert system, whose operations are just those of Boolean algebra and whose theorems are Boolean tautologies, those Boolean terms equal to the Boolean constant 1. Another form is sequent calculus, which has two sorts, propositions as in ordinary propositional calculus, and pairs of lists of propositions called sequents, such as "A"∨"B", "A"∧"C"... formula_8 "A", "B"→"C"... The two halves of a sequent are called the antecedent and the succedent respectively. The customary metavariable denoting an antecedent or part thereof is Γ, and for a succedent Δ; thus Γ,"A" formula_8 Δ would denote a sequent whose succedent is a list Δ and whose antecedent is a list Γ with an additional proposition "A" appended after it. The antecedent is interpreted as the conjunction of its propositions, the succedent as the disjunction of its propositions, and the sequent itself as the entailment of the succedent by the antecedent.


title: Boolean algebra

text: Entailment differs from implication in that whereas the latter is a binary "operation" that returns a value in a Boolean algebra, the former is a binary "relation" which either holds or does not hold. In this sense entailment is an "external" form of implication, meaning external to the Boolean algebra, thinking of the reader of the sequent as also being external and interpreting and comparing antecedents and succedents in some Boolean algebra. The natural interpretation of formula_8 is as ≤ in the partial order of the Boolean algebra defined by "x" ≤ "y" just when "x"∨"y" = "y". This ability to mix external implication formula_8 and internal implication → in the one logic is among the essential differences between sequent calculus and propositional calculus.


title: Boolean algebra

text: Boolean algebra as the calculus of two values is fundamental to computer circuits, computer programming, and mathematical logic, and is also used in other areas of mathematics such as set theory and statistics.


title: Boolean algebra

text: In the early 20th century, several electrical engineers intuitively recognized that Boolean algebra was analogous to the behavior of certain types of electrical circuits. Claude Shannon formally proved such behavior was logically equivalent to Boolean algebra in his 1937 master's thesis, "A Symbolic Analysis of Relay and Switching Circuits".


title: Boolean algebra

text: Today, all modern general purpose computers perform their functions using two-value Boolean logic; that is, their electrical circuits are a physical manifestation of two-value Boolean logic. They achieve this in various ways: as voltages on wires in high-speed circuits and capacitive storage devices, as orientations of a magnetic domain in ferromagnetic storage devices, as holes in punched cards or paper tape, and so on. (Some early computers used decimal circuits or mechanisms instead of two-valued logic circuits.)


title: Boolean algebra

text: Of course, it is possible to code more than two symbols in any given medium. For example, one might use respectively 0, 1, 2, and 3 volts to code a four-symbol alphabet on a wire, or holes of different sizes in a punched card. In practice, the tight constraints of high speed, small size, and low power combine to make noise a major factor. This makes it hard to distinguish between symbols when there are several possible symbols that could occur at a single site. Rather than attempting to distinguish between four voltages on one wire, digital designers have settled on two voltages per wire, high and low.


title: Boolean algebra

text: Computers use two-value Boolean circuits for the above reasons. The most common computer architectures use ordered sequences of Boolean values, called bits, of 32 or 64 values, e.g. 01101000110101100101010101001011. When programming in machine code, assembly language, and certain other programming languages, programmers work with the low-level digital structure of the data registers. These registers operate on voltages, where zero volts represents Boolean 0, and a reference voltage (often +5 V, +3.3 V, +1.8 V) represents Boolean 1. Such languages support both numeric operations and logical operations. In this context, "numeric" means that the computer treats sequences of bits as binary numbers (base two numbers) and executes arithmetic operations like add, subtract, multiply, or divide. "Logical" refers to the Boolean logical operations of disjunction, conjunction, and negation between two sequences of bits, in which each bit in one sequence is simply compared to its counterpart in the other sequence. Programmers therefore have the option of working in and applying the rules of either numeric algebra or Boolean algebra as needed. A core differentiating feature between these families of operations is the existence of the carry operation in the first but not the second.


title: Boolean algebra

text: Other areas where two values is a good choice are the law and mathematics. In everyday relaxed conversation, nuanced or complex answers such as "maybe" or "only on the weekend" are acceptable. In more focused situations such as a court of law or theorem-based mathematics however it is deemed advantageous to frame questions so as to admit a simple yes-or-no answer—is the defendant guilty or not guilty, is the proposition true or false—and to disallow any other answer. However much of a straitjacket this might prove in practice for the respondent, the principle of the simple yes-no question has become a central feature of both judicial and mathematical logic, making two-valued logic deserving of organization and study in its own right.


title: Boolean algebra

text: A central concept of set theory is membership. Now an organization may permit multiple degrees of membership, such as novice, associate, and full. With sets however an element is either in or out. The candidates for membership in a set work just like the wires in a digital computer: each candidate is either a member or a nonmember, just as each wire is either high or low.


title: Boolean algebra

text: Algebra being a fundamental tool in any area amenable to mathematical treatment, these considerations combine to make the algebra of two values of fundamental importance to computer hardware, mathematical logic, and set theory.


title: Boolean algebra

text: Two-valued logic can be extended to multi-valued logic, notably by replacing the Boolean domain {0, 1} with the unit interval [0,1], in which case rather than only taking values 0 or 1, any value between and including 0 and 1 can be assumed. Algebraically, negation (NOT) is replaced with 1 − "x", conjunction (AND) is replaced with multiplication (formula_12), and disjunction (OR) is defined via De Morgan's law. Interpreting these values as logical truth values yields a multi-valued logic, which forms the basis for fuzzy logic and probabilistic logic. In these interpretations, a value is interpreted as the "degree" of truth – to what extent a proposition is true, or the probability that the proposition is true.


title: Boolean algebra

text: The original application for Boolean operations was mathematical logic, where it combines the truth values, true or false, of individual formulas.


title: Boolean algebra

text: Natural languages such as English have words for several Boolean operations, in particular conjunction ("and"), disjunction ("or"), negation ("not"), and implication ("implies"). "But not" is synonymous with "and not". When used to combine situational assertions such as "the block is on the table" and "cats drink milk," which naively are either true or false, the meanings of these logical connectives often have the meaning of their logical counterparts. However, with descriptions of behavior such as "Jim walked through the door", one starts to notice differences such as failure of commutativity, for example the conjunction of "Jim opened the door" with "Jim walked through the door" in that order is not equivalent to their conjunction in the other order, since "and" usually means "and then" in such cases. Questions can be similar: the order "Is the sky blue, and why is the sky blue?" makes more sense than the reverse order. Conjunctive commands about behavior are like behavioral assertions, as in "get dressed and go to school". Disjunctive commands such "love me or leave me" or "fish or cut bait" tend to be asymmetric via the implication that one alternative is less preferable. Conjoined nouns such as "tea and milk" generally describe aggregation as with set union while "tea or milk" is a choice. However context can reverse these senses, as in "your choices are coffee and tea" which usually means the same as "your choices are coffee or tea" (alternatives). Double negation as in "I don't not like milk" rarely means literally "I do like milk" but rather conveys some sort of hedging, as though to imply that there is a third possibility. "Not not P" can be loosely interpreted as "surely P", and although "P" necessarily implies "not not "P"" the converse is suspect in English, much as with intuitionistic logic. In view of the highly idiosyncratic usage of conjunctions in natural languages, Boolean algebra cannot be considered a reliable framework for interpreting them.


title: Boolean algebra

text: Boolean operations are used in digital logic to combine the bits carried on individual wires, thereby interpreting them over {0,1}. When a vector of "n" identical binary gates are used to combine two bit vectors each of "n" bits, the individual bit operations can be understood collectively as a single operation on values from a Boolean algebra with 2 elements.


title: Boolean algebra

text: Naive set theory interprets Boolean operations as acting on subsets of a given set "X". As we saw earlier this behavior exactly parallels the coordinate-wise combinations of bit vectors, with the union of two sets corresponding to the disjunction of two bit vectors and so on.


title: Boolean algebra

text: The 256-element free Boolean algebra on three generators is deployed in computer displays based on raster graphics, which use bit blit to manipulate whole regions consisting of pixels, relying on Boolean operations to specify how the source region should be combined with the destination, typically with the help of a third region called the mask. Modern video cards offer all 2 = 256 ternary operations for this purpose, with the choice of operation being a one-byte (8-bit) parameter. The constants SRC = 0xaa or 10101010, DST = 0xcc or 11001100, and MSK = 0xf0 or 11110000 allow Boolean operations such as (SRC^DST)&MSK (meaning XOR the source and destination and then AND the result with the mask) to be written directly as a constant denoting a byte calculated at compile time, 0x80 in the (SRC^DST)&MSK example, 0x88 if just SRC^DST, etc. At run time the video card interprets the byte as the raster operation indicated by the original expression in a uniform way that requires remarkably little hardware and which takes time completely independent of the complexity of the expression.


title: Boolean algebra

text: Solid modeling systems for computer aided design offer a variety of methods for building objects from other objects, combination by Boolean operations being one of them. In this method the space in which objects exist is understood as a set "S" of voxels (the three-dimensional analogue of pixels in two-dimensional graphics) and shapes are defined as subsets of "S", allowing objects to be combined as sets via union, intersection, etc. One obvious use is in building a complex shape from simple shapes simply as the union of the latter. Another use is in sculpting understood as removal of material: any grinding, milling, routing, or drilling operation that can be performed with physical machinery on physical materials can be simulated on the computer with the Boolean operation "x" ∧ ¬"y" or "x" − "y", which in set theory is set difference, remove the elements of "y" from those of "x". Thus given two shapes one to be machined and the other the material to be removed, the result of machining the former to remove the latter is described simply as their set difference.


title: Boolean algebra

text: Search engine queries also employ Boolean logic. For this application, each web page on the Internet may be considered to be an "element" of a "set". The following examples use a syntax supported by Google.


title: Frank-Walter Steinmeier

text: Frank-Walter Steinmeier (; born 5 January 1956) is a German politician serving as President of Germany since 19 March 2017. He was previously Federal Minister of Foreign Affairs from 2005 to 2009 and again from 2013 to 2017, as well as Vice Chancellor of Germany from 2007 to 2009. Steinmeier was chairman-in-office of the Organization for Security and Co-operation in Europe (OSCE) in 2016.


title: Frank-Walter Steinmeier

text: Steinmeier is a member of the Social Democratic Party of Germany (SPD), holds a doctorate in law and was formerly a career civil servant. He was a close aide of Gerhard Schröder when Schröder was Prime Minister of Lower Saxony during most of the 1990s, and served as Schröder's chief of staff from 1996. When Schröder became Chancellor of Germany in 1998, Steinmeier was appointed Under-Secretary of State in the German Chancellery with the responsibility for the intelligence services. From 1999 to 2005 he served as Chief of Staff of the Chancellery.


title: Frank-Walter Steinmeier

text: Following the 2005 federal election, Steinmeier became Foreign Minister in the first grand coalition government of Angela Merkel, and from 2007 he additionally held the office of vice chancellor. In 2008, he briefly served as acting chairman of his party. He was the SPD's candidate for chancellor in the 2009 federal election, but his party lost the election and he left the federal cabinet to become leader of the opposition. Following the 2013 federal election, he again became Minister for Foreign Affairs in Merkel's second grand coalition. In November 2016 he was announced as the candidate for President of Germany of the governing coalition, consisting of his own party and the CDU/CSU, and thus became the presumptive electee, as the coalition held a large majority in the Federal Convention. He left the cabinet on 27 January 2017. He was elected president by the Federal Convention on 12 February 2017 with 74% of the vote. On 13 February 2022, he was re-elected by the Federal Convention for a second and final term with 78% of the vote.


title: Frank-Walter Steinmeier

text: Steinmeier belongs to the right wing of the SPD, known as reformists and moderates. As chief of staff he was a principal architect of Agenda 2010, the Schröder government's reforms of the welfare state. His lenient policies toward countries such as Russia and China have earned him criticism both in Germany and internationally, and he has been criticized for prioritizing German business interests over human rights.


title: Frank-Walter Steinmeier

text: Steinmeier was born in 1956 in Detmold. Although his full name is Frank-Walter, his friends call him Frank.


title: Frank-Walter Steinmeier

text: His father, a carpenter, was affiliated with the Church of Lippe (one of Germany's few Calvinist regional church bodies, and a member church of the Evangelical Church of Germany). His mother, born in Breslau (now Wrocław, Poland), came as a refugee from a Lutheran part of Silesia during the flight and expulsion of Germans after World War II.


title: Frank-Walter Steinmeier

text: Following his "Abitur", Steinmeier did his military service from 1974 to 1976, then studied law and political science at the Justus Liebig University Giessen, where Brigitte Zypries was a fellow student. In 1982 he passed his first and in 1986 his second state examination in law.


title: Frank-Walter Steinmeier

text: Steinmeier worked as a scientific assistant to the professor of public law and political science at Giessen University until he obtained his doctorate of law in 1991. His dissertation explored the state's role in preventing homelessness.


title: Frank-Walter Steinmeier

text: Steinmeier is married and has one daughter. On 24 August 2010, he donated a kidney to his wife, Elke Büdenbender.


title: Frank-Walter Steinmeier

text: In 2015, Steinmeier served as best man at the wedding of Rüdiger Grube and Cornelia Poletto in Hamburg.


title: Frank-Walter Steinmeier

text: Steinmeier is a Reformed Protestant and an active member of the Reformed Bethlehem congregation in Berlin-Neukölln. He was baptized into his father's church (the Church of Lippe) as a youth.


title: Frank-Walter Steinmeier

text: Steinmeier became an adviser in 1991 for Law of Communication media and media guidelines in the State Chancellery of Lower Saxony in Hanover. In 1993, he became director of the Personal Office for the prime minister of Lower Saxony, Gerhard Schröder. In 1996, he became the Secretary of State and head of the State Chancellery of Lower Saxony.


title: Frank-Walter Steinmeier

text: Steinmeier was appointed in November 1998 as Secretary of State, a junior Chancellery bureaucrat, and Commissioner for the Federal Intelligence Services at the office of the chancellor following Schröder's election victory. He replaced Bodo Hombach as the head of the office of the chancellor in 1999, after the later entered European Union politics. He held onto his Secretary of State rank and therefore was the only Head of the Chancellery to not be appointed Minister for Special Affairs, i. e. does not have cabinet rank, from 1984 to today. During this period Steinmeier was also one of the advisors to Schröder. He was crucial in securing a red-green majority in parliament for Schröder's contentious "Agenda 2010" of economic reforms. Because of his effective management beyond the spotlight of politics, he was nicknamed "Die Graue Effizienz" (The Grey Efficiency) —a pun on "Graue Eminenz", the German for éminence grise.


title: Frank-Walter Steinmeier

text: As Commissioner for the Federal Intelligence Services (a title often held by the Head of the Chancellery) Steinmeier was responsible for co-ordinating Germany's intelligence services. In 2003, he supported Schröder in his controversial decision to forge a coalition with Russia and France against the U.S.-led war against Iraq. Meanwhile, he approved the decision to install a German intelligence officer in the Qatar-based office of General Tommy Franks, the American commander of the U.S. invasion in Iraq, who passed on to the United States information being gathered in Baghdad by two German intelligence officers operating there.


title: Frank-Walter Steinmeier

text: In 2004, Steinmeier participated in diplomatic negotiations settling on compensation payments with Libya for victims of the 1986 terrorist bombing of the LaBelle disco in Berlin.


title: Frank-Walter Steinmeier

text: A major controversy during Steinmeier's term as chief of staff was the imprisonment of a German-born Turk, Murat Kurnaz, in Guantánamo Bay from 2002 until August 2006. Steinmeier denied during a parliamentary inquiry in March 2007 that he had blocked Kurnaz's release. Instead, he claimed that Berlin had feared Kurnaz was a threat and should go to Turkey, not Germany, if released. Only after Merkel's election was Kurnaz released and brought back to Germany.


title: Frank-Walter Steinmeier

text: On 22 November 2005, after the 2005 federal elections, Steinmeier became Minister of Foreign Affairs in the Grand coalition cabinet led by Angela Merkel. He was the first SPD Foreign Minister since Willy Brandt (1966–1969).


title: Frank-Walter Steinmeier

text: Upon taking office, Steinmeier led the preparations for Germany taking over the rotating presidency of the Council of the European Union in the first half of 2007.


title: Frank-Walter Steinmeier

text: Following Franz Müntefering's departure from the cabinet on 21 November 2007, Steinmeier also filled the position of Vice-Chancellor.


title: Frank-Walter Steinmeier

text: During his time in office, Steinmeier was widely regarded as having good working relations with Angela Merkel but often taking a different stance on foreign affairs. By and large, he allowed Merkel to set the pace in foreign policy., working harmoniously with her on a range of foreign policy issues, from confronting Iran over its nuclear program to negotiating binding goals to combat climate change. In one significant foreign-policy disagreement, Steinmeier held in 2009 that Germany should by 2013 lay the groundwork for withdrawing its troops from Afghanistan, a deployment that around two-thirds of Germans opposed by then. Unlike Merkel, he also favored Turkish entry into the European Union.


title: Frank-Walter Steinmeier

text: Also, Steinmeier became known for his rather Russia-friendly stance, arguing strenuously for engagement with the increasingly assertive power to the east, rather than its isolation. He formulated a policy toward Russia deliberately reminiscent of "Ostpolitik", the eastward-facing policy pioneered by Chancellor Willy Brandt in the early 1970s. Together with Gernot Erler, the SPD's leading Russia expert and the deputy foreign minister, Steinmeier initiated Germany's so-called Partnership for Modernization with Russia (announced in 2008), which became an official EU policy in 2010. Pressed by lawmakers to say more on his attitude toward Russia in the wake of the high-profile murders of opposition figures Anna Politkovskaya and Alexander Litvinenko at a 2007 hearing at the European Parliament, Steinmeier stated that "[t]here is a certain trend toward [media] hysterics and one needs to get a sense of reason back into the debate". In May 2008, he became the first foreign official to hold talks with President Dmitri Medvedev and Prime Minister Vladimir Putin after they took up their new positions following the 2008 presidential elections.


title: Frank-Walter Steinmeier

text: In 2006, "Foreign Affairs" published an analysis of the state of US and Russian nuclear forces, concluding that post-Cold War US nuclear forces seemed designed to carry out a preemptive strike against Russia or China and that the planned missile defense would be valuable primarily in an offensive context as an adjunct to a US first-strike capability. The article elicited a semi-official Russian response from ex-PM Yegor Gaidar in the "Financial Times" a few days later. In 2007, the US government reportedly was reportedly deeply irritated, although publicly silent, about Steinmeier, who had sounded supportive of Russian accusations that a planned US missile defense complex in Poland would upset the strategic balance in Europe – and who then left without challenge Russian General Nikolai Solovtsov's threat of retaliation against Poland and the Czech Republic if they deployed U.S. defensive systems. Russian opposition activists later celebrated when Steinmeier and the SDP lost the 2009 election, signaling their discontent with Steinmeier. Oleg Petrovich Orlov, head of the Memorial human rights group, said that Steinmeier had prolonged Schröder's policies on Russia and that Germany's policies were "extremely bad for civil society, democracy and the country as a whole".


title: Frank-Walter Steinmeier

text: In February 2009, Steinmeier became the first member of Merkel's cabinet to be received by the incoming Obama administration.


title: Frank-Walter Steinmeier

text: During his time in office, Steinmeier managed to extract German hostages from Iraq and Yemen. In 2007, he also succeeded in securing the release of a German citizen who was imprisoned in Iran for illegally entering the country's waters on a fishing expedition.


title: Frank-Walter Steinmeier

text: Steinmeier served as acting chairman of the SPD from 7 September 2008 to 18 October 2008. Domestically, throughout his term he was the only major politician with approval ratings consistently as high as or higher than Merkel's. This was helped by the especially high ratings foreign ministers generally receive in Germany.


title: Frank-Walter Steinmeier

text: On 7 September 2008, following the resignation of SPD chairman Kurt Beck, Steinmeier was chosen as the SPD candidate for chancellor for the 2009 federal elections and also designated as acting SPD Chairman, pending the return of Müntefering to that position. In his election campaign, he argued for new tax rules to deter high executive pay and bonuses, and for minimum wages to slow the growing gap between Germany's highest and lowest earners. He also focused on improving public healthcare.


title: Frank-Walter Steinmeier

text: During his time as leader of the parliamentary opposition, Steinmeier regularly accused Angela Merkel's government of increasing the national debt and pandering to the rich. In 2011, Steinmeier argued that Merkel's decision to appoint her economics adviser, Jens Weidmann, to be the next head of Bundesbank undermined the political independence and public trust in the German central bank.


title: Frank-Walter Steinmeier

text: In late 2012, Steinmeier was once again considered a possible candidate to challenge Chancellor Angela Merkel in the 2013 general election, but soon withdrew from the contest. As a consequence, SPD chairman Sigmar Gabriel later announced that the leadership agreed to nominate Peer Steinbrück.


title: Frank-Walter Steinmeier

text: After the elections of 2013 and the new grand coalition government, Steinmeier was appointed foreign minister for a second time in December 2013. He replaced Guido Westerwelle, who had signed the P5+1 accord with Iran in November 2013. His deputies are Michael Roth (SPD) and Maria Böhmer (CDU). Upon taking office, Steinmeier initiated an ambitious review of Germany's foreign policy, holding meetings nationwide and drawing in more than 12,000 people who work at the ministry or abroad.


title: Frank-Walter Steinmeier

text: Over the course of 2014, Steinmeier alternated with Merkel as Germany's most popular politician in polls of eligible voters.


title: Frank-Walter Steinmeier

text: In light of criticism from the United States, Steinmeier has stood firm on Germany's approach in the Ukraine conflict, where it was balancing support for European economic sanctions on Russia with leaving the door open to a revived partnership. In May 2014, he proposed a greater mediation role for the OSCE, including the convening of local "round table" talks in Ukraine to defuse conflicts. Between 2015 and 2016, Steinmeier hosted a series of Normandy format meetings in Berlin to negotiate a solution of the situation in the East of Ukraine. During the Minsk II talks on a ceasefire for eastern Ukraine in early 2015, he successfully negotiated with Russian President Vladimir Putin on allowing German doctors to visit Ukrainian military pilot Nadiya Savchenko, who had been on hunger strike for more than two months in a Russian jail. Steinmeier has in the past repeatedly ruled out arms shipments to resolve the yearlong conflict.


title: Frank-Walter Steinmeier

text: In 2015, Steinmeier hosted a meeting of the delegations from Libya's two rival governments, who were battling for control of the country, and United Nations Special Representative Bernardino León to discuss a UN-sponsored peace and power-sharing proposal despite splits among some of the parties.


title: Frank-Walter Steinmeier

text: Steinmeier later was instrumental in convening the International Syria Support Group (ISSG) and the Syria peace talks in Vienna in October 2015, drawing together Saudi Arabia; its main regional rival, Iran; as well as Russia, the United States and other Western powers and regional actors including Turkey and Iraq.


title: Frank-Walter Steinmeier

text: President Joachim Gauck announced in June 2016 that he would not run for re-election, resulting in a search for a candidate to succeed him. In November 2016, Chancellor Angela Merkel's conservatives agreed with the Social Democrats to support Steinmeier's candidacy for president in the presidential election, scheduled for 12 February 2017.


title: Frank-Walter Steinmeier

text: Merkel had originally wanted to nominate Green politician Marianne Birthler, and as the CDU/CSU and the Greens control a majority in the Federal Convention, Birthler's election would have been secured. However, Birthler after some time decided not to run.


title: Frank-Walter Steinmeier

text: On 12 February 2017 Germany's 16th Federal Convention elected Steinmeier President on the first ballot, with 931 votes out of a total of 1,260.


title: Frank-Walter Steinmeier

text: Steinmeier took office as President of Germany on 19 March 2017, after the expiration of his predecessor's term in office, and on 22 March 2017 he took the oath that newly invested presidents must take before a joint session of the Bundestag and the Bundesrat, according to the Basic Law. On the 13 February 2022 he was re-elected as president.


title: Frank-Walter Steinmeier

text: Following the federal election in September 2017, coalition talks began between the Christian Democratic Union, Christian Social Union, Free Democratic Party and the Green Party. The talks continued for 4 weeks until just past midnight on 20 November when the Free Democrats and their leader Christian Lindner walked out of the talks and they subsequently collapsed. The collapse of the talks left another Grand Coalition as the only coalition with a majority in the Bundestag; this however seemed difficult, as the Leader of the Social Democratic Party Martin Schulz had ruled out another Grand Coalition on multiple occasions. In the following weeks, Steinmeier played an important role in the formation of the next government. This is because if the Bundestag fails to elect a chancellor in 14 days of voting, the president can either appoint the individual with most votes to lead a minority government or dissolve the Bundestag and call new elections. This type of political crisis had never been seen in Germany before and pushed the president into a quite powerful position which is rare for Germany. Steinmeier declared he would not consider a dissolution of the Bundestag as a preferable solution, and managed to persuade Schulz to meet with Angela Merkel and start preliminary talks. After long coalition talks, CDU, CSU and SPD formed a new grand coalition. Merkel was re-elected in the Bundestag on 14 March 2018.


title: Frank-Walter Steinmeier

text: In the past, "Human Rights Watch" has labeled Steinmeier as "Realpolitik advocate", for whom, "when it comes to defining his relationship with countries" such as Russia, China, Iran and Saudi Arabia, "human rights play only a subordinate role".


title: Frank-Walter Steinmeier

text: In Steinmeier's opinion, the "[r]ejection of capital punishment is one of the keystones of German human-rights policy. The death penalty goes against our fundamental ethic and moral principles". He personally called for the abolition of the death penalty in Uzbekistan; capital punishment in Uzbekistan has been abolished since 2008. In April 2014, he summoned the Egyptian ambassador Mohamed Higazy after a Cairo court sentenced 683 individuals to death for inciting violence during protests in summer 2013, following the military overthrow of elected President Mohammed Morsi. Following the 2016 Turkish coup d'état attempt, he warned that any move by Turkey to reinstate the death penalty would derail its efforts to join the European Union. He criticized the 2016–present purges in Turkey.


title: Frank-Walter Steinmeier

text: In response to the protests following the 2009 Iranian presidential election against the disputed victory of Iranian President Mahmoud Ahmadinejad, Steinmeier condemned what he called "brutal actions" against demonstrators in Tehran and summoned the Iranian ambassador Alireza Sheikhattar to explain.


title: Frank-Walter Steinmeier

text: After Germany had only narrowly managed to avoid a deficit warning from the European Commission in 2002, Schröder and Steinmeier became the driving forces behind weakening the Stability and Growth Pact, a rule-based framework for the coordination of national fiscal policies originally intended as the guarantor of a stable euro.


title: Frank-Walter Steinmeier

text: In a joint article in the "Financial Times" on 14 December 2010, Steinmeier and Peer Steinbrück proposed to solve the European debt crisis with "a combination of a haircut for debt holders, debt guarantees for stable countries and the limited introduction of European-wide bonds in the medium term, accompanied by more aligned fiscal policies". In February 2011, Steinmeier proposed Steinbrück as a candidate to lead the European Central Bank.


title: Frank-Walter Steinmeier

text: Under Steinmeier's parliamentary leadership, the Social Democrats raised pressure on Chancellor Angela Merkel to agree to more burden-sharing to stem the euro zone crisis, repeatedly calling on her to assume greater risks to avert a breakup of the single currency. In both February and November 2012, his parliamentary group voted largely in favour of the Merkel government's proposal for eurozone bailout packages for Greece, while criticizing the measures as being "not an enduring solution for the Greeks". In July 2014, he helped build the opposition's support for a euro zone rescue package for Spanish banks. Later, as foreign minister, he publicly advised against "frivolous" talk of a Greek withdrawal from the eurozone, calling for a serious search for a solution.


title: Frank-Walter Steinmeier

text: Reacting to a growth of euro-skeptic political parties across Europe by early 2014, Steinmeier offered the United Kingdom limited support on renegotiating the Treaties of the European Union, saying Germany wanted to see Britain's influence in the "midst" of the EU, not on "the sidelines". After Britain's vote to leave the EU in 2016, he argued that the union lacked the cohesion to undertake major new integration steps and should instead focus on migration, high youth unemployment and security.


title: Frank-Walter Steinmeier

text: At the same time, Steinmeier worked to develop new formats and revive new ones. In December 2014, he met with the foreign ministers from the three Nordic countries Denmark, Finland and Sweden – Margot Wallström, Erkki Tuomioja and Martin Lidegaard – for the so-called "N3 + 1" format to discuss issues of common concern for the first time.


title: Frank-Walter Steinmeier

text: In August 2016, he joined French foreign minister Jean-Marc Ayrault in pledging to "reinvigorate" the Weimar Triangle and published a document 'A strong Europe in a world of uncertainties'.


title: Frank-Walter Steinmeier

text: Between 2014 and 2016, he visited the three Baltic states – Estonia, Latvia and Lithuania – six times, the highest number of visits by any German Foreign Minister.


title: Frank-Walter Steinmeier

text: Also in late 2014, Steinmeier and his British counterpart Philip Hammond united in a bid to end a deadlock in relations between Bosnia and the European Union, arguing that the EU should abandon its insistence on changes to Bosnia's electoral code as a precondition for a Stabilization and Association Agreement on the path to EU membership.


title: Frank-Walter Steinmeier

text: In 2007, Steinmeier said he opposes European Commission proposals on unbundling the ownership of energy networks in the European Union, as it was proposed in the Third Energy Package.


title: Frank-Walter Steinmeier

text: On 14 May 2014, Steinmeier became the first German foreign minister to attend a meeting of the French cabinet. Together with his French counterpart Laurent Fabius, he flew on several joint diplomatic missions between 2014 and 2015, including to Moldova, Georgia, Tunisia, Nigeria and Bangladesh. In 2016, he joined Fabius' successor Jean-Marc Ayrault for trips to Ukraine, Libya, Mali and Niger.


title: Frank-Walter Steinmeier

text: In May 2007, the daily "Financial Times Deutschland" reported that Steinmeier had served as mediator in the so-called Bronze Night controversy, an Estonia-Russia dispute over the removal of a Red Army memorial in Tallinn. According to the report, Steinmeier suggested the Estonian ambassador to Russia, Marina Kaljurand, go on vacation in an effort to calm the situation. Steinmeier called his Russian counterpart Sergei Lavrov to suggest not only that Kaljurand take a holiday, but also that Russia drop the dispute for the time being. After speaking with Lavrov, Steinmeier reportedly called Estonian Foreign Minister Urmas Paet and got him to agree to the deal. Kaljurand left Moscow for a two-week vacation and pro-Kremlin youth activists blockading the Estonian embassy in Moscow ended their protests the same day.


title: Frank-Walter Steinmeier

text: Upon returning to government in late 2013, Steinmeier criticized Russia in his inaugural speech for exploiting Ukraine's economic plight to prevent it from signing the Ukraine–European Union Association Agreement. In March 2014, he defended Russia's membership of the G8, saying "The format of the G8 is actually the only one in which we in the West can speak directly with Russia." When Germany held the chairmanship of the group in 2015, he maintained that excluding Russia over its actions in Ukraine was a necessary step but not a goal in itself; citing the Middle East, he argued that "a look at the world shows that we need Russia as a constructive partner in a number of conflicts".


title: Frank-Walter Steinmeier

text: In a 2015 letter to Cecilia Malmström, the EU's trade chief, Steinmeier proposed a joint declaration between the EU and Russia offering Moscow the prospect of long-sought investment and energy concessions to create a more integrated economic area from the Atlantic to the Pacific. According to the letter, "by the content of this declaration we could respond to Russia's wishes and begin a closer exchange of views on energy and investment protection issues, even if the Ukraine–European Union Association Agreement does not directly touch on them".


title: Frank-Walter Steinmeier

text: In June 2016, Steinmeier criticised NATO 'warmongering' on Russia: "The one thing we shouldn't do now is inflame the situation with loud sabre-rattling and warmongering." The CDU politicians Volker Bouffier and Herbert Reul criticised him for his stance on Russia, while his comments were welcomed by the Russian media.


title: Frank-Walter Steinmeier

text: Shortly after the 2022 Russian invasion of Ukraine, Steinmeier expressed regret for his earlier stance on Russia, saying his years of support for the Nord Stream 2 gas pipeline had been a clear mistake. He called for a war crimes tribunal against Russian President Vladimir Putin and Russian Foreign Minister Sergei Lavrov. Steinmeier said that he "wrongly believed that Vladimir Putin would not precipitate a complete economic, political, and moral devastation of his country because of his imperial mania."


title: Frank-Walter Steinmeier

text: Steinmeier voiced his support for Barack Obama when Obama was still a presidential candidate, and supported Obama's wish to deliver a speech before the iconic Brandenburg Gate during the 2008 U.S. presidential campaign.


title: Frank-Walter Steinmeier

text: In 2016 Steinmeier described then-U.S. presidential candidate Donald Trump as a "hate preacher". After Trump's election, Steinmeier refused to congratulate him, and condemned Trump's views. He has been described as "the German government's most strident detractor" of Trump.


title: Frank-Walter Steinmeier

text: During a 2006 meeting with Turkmen President Saparmurat Niyazov, Steinmeier criticized Turkmenistan for its slow progress in implementing the rule of law and human rights and said that the state's progress in carrying out political reforms had been "too halting".


title: Frank-Walter Steinmeier

text: When Germany chaired a United Nations group aimed at resolving 2008 Russo-Georgian diplomatic crisis, Steinmeier presented to the three conflict parties – Georgia, Abkhazia and Russia – a plan which included a three-stage peace proposal, entailing an end to violence, confidence-building measures over the following year that could lead to the resumption of direct talks between Georgia and Abkhazia, and the return of about 250,000 Georgian refugees to Abkhazia. However, both Georgia and Abkhazia rejected the proposal. In September 2008, Steinmeier called for an international probe into the conflict over Georgia's breakaway provinces. During a 2014 visit to the country, he reiterated that membership of NATO and of the EU would remain off the cards for a long while to come.


title: Frank-Walter Steinmeier

text: In August 2006, Steinmeier made his first visit to Afghanistan, where Germany had taken over the command of the 21,000-strong NATO-led International Security Assistance Force (ISAF) shortly before. Ahead of the 2009 federal elections, Steinmeier – then still in his capacity as foreign minister – commissioned an internal report on Germany's engagement in Afghanistan which recommended that Germany should start pulling out of the country within four years; at the time, this was seen as a stark departure from Steinmeier's earlier insistence Germany should not set a date for withdrawing its then 4,200-strong contingent from the north of Afghanistan as the move could play into the hands of Taliban insurgents.


title: Frank-Walter Steinmeier

text: In October 2014, Steinmeier visited both Armenia and Azerbaijan to facilitate a negotiated solution to the long-standing conflict over Nagorny Karabakh, a region of Azerbaijan controlled by ethnic Armenians. In 2016, he returned to both countries to in his capacity as chairman of the Organization for Security and Co-operation in Europe (OSCE) to reinvigorate the talks.


title: Frank-Walter Steinmeier

text: In the Israeli–Palestinian conflict, Steinmeier supports a two-state solution and calls for an end to the Israeli occupation of the Palestinian territories. He welcomed the United Nations Security Council Resolution 2334 and said the Israeli settlements on occupied territory form an obstacle to peace and a two-state solution. He further said that "a democratic Israel is achievable only through a two-state-solution". Steinmeier praised the speech by US Secretary of State John Kerry which outlined the United States' position on the Israeli–Palestinian conflict in December 2016; in the speech Kerry said a peace agreement must be based on the 1967 lines, that all citizens must enjoy equal rights, that occupation must end, that the Palestinian refugee issue must be resolved, and that Jerusalem must be the capital of both states, and criticised the Netanyahu government's agenda as driven by "extreme elements".


title: Frank-Walter Steinmeier

text: Steinmeier is a staunch proponent of the Iran nuclear deal framework, and has called the agreement "an opening for further diplomatic endeavors".


title: Frank-Walter Steinmeier

text: Steinmeier has visited the Zaatari refugee camp in Jordan twice to learn more about the plight of Syrians fleeing the violence in the ongoing Syrian civil war that erupted in 2011, first in his capacity as chairman of the SPD parliamentary group in May 2013 and later as foreign minister in May 2015. In early 2014, upon taking office as foreign minister, he agreed with Chancellor Angela Merkel and Defence Minister Ursula von der Leyen that Germany would help destroy Syria's arsenal of chemical weapons materials as part of an international disarmament program. In October 2014, he co-chaired the Berlin Conference on the Syrian Refugee Situation along with Development Minister Gerd Müller and the UN High Commissioner for Refugees, António Guterres.


title: Frank-Walter Steinmeier

text: In March 2015, Steinmeier said he "can understand" Saudi Arabia's decision to mount a military intervention in Yemen and acknowledged the operation had "support from the region". However, he said the crisis could not be solved by violence and urged a negotiated solution.


title: Frank-Walter Steinmeier

text: Steinmeier has rejected claims for war reparations from the Greek Syriza party in response to Germany's position on the Greek government-debt crisis. When incoming Greek Prime Minister Alexis Tsipras, in his first major speech to parliament in early 2015, pledged to seek war reparations from Germany, Steinmeier replied to Greek Foreign Minister Nikos Kotzias that Germany was fully aware of its political and moral responsibility for the "terrible events" in Greece between 1941 and 1944 when German troops occupied the country. "Still, we are firmly convinced that all reparations issues, including forced loans, are judicially settled once-and-for-all," Steinmeier said.


title: Frank-Walter Steinmeier

text: Steinmeier openly attacked Merkel over her 2007 meeting with the Dalai Lama, accusing the chancellor of "playing to public opinion" without regard for the effectiveness of the meeting in improving political or religious rights on the ground in China. In 2008, he refused to meet the Dalai Lama during his five-day visit, arguing that such a meeting could undermine international efforts to promote sustained contact between China and Tibet. Instead, Steinmeier issued the statement "it takes a lot of courage not to meet with the Dalai Lama these days", which "The New York Times" described as "extraordinarily cynical" and accused Steinmeier of prioritizing business interests over human rights.


title: Frank-Walter Steinmeier

text: In the case of Murat Kurnaz, innocently imprisoned in 2002 and tortured by the US, Steinmeier allegedly had an offer by the United States Department of Defense and the CIA already in September 2002 regarding a transfer of Murat Kurnaz to Germany, where he was born and raised. Kurnaz had been first sold as a terror suspect in Pakistan, then imprisoned in Afghanistan and later in Guantanamo Bay Naval Base, Cuba, until 2006. By refusing the offer Steinmeier is thought to have been politically directly responsible for his continued imprisonment.


title: Frank-Walter Steinmeier

text: During a 2015 debate about Germany's recognition of the Armenian genocide on the occasion of its centenary, Steinmeier was the politician most reluctant to endorse it, mainly because of Germany's relations with Turkey. He was widely criticized for his position and accused of Armenian genocide denial. When the German Bundestag almost unanimously approved a resolution in 2016 that recognises the killings of up to 1.5 million Armenians by Ottoman forces as a genocide, a description that Turkey strongly rejects, Steinmeier abstained from the vote and criticized the resolution in public; Steinmeier was one of only two of the 630 members of parliament who did not support the resolution. And Steinmeier alleged that calling Armenian massacres genocide risks belittling the Holocaust.


title: Frank-Walter Steinmeier

text: Following the 2013 elections, Steinmeier became the first prominent member of the Social Democrats to be confronted with allegations that he plagiarized parts of his 1991 doctoral dissertation about the role of the state in the prevention of homelessness. Similar accusations had previously led to the resignation of two ministers of the Merkel government. In response, Steinmeier rejected the charges and said that he had asked the University of Giessen to check his dissertation for unacknowledged citations. In May 2013, a university committee for safeguarding academic practices found that Steinmeier had no fraudulent intent and had not committed academic misconduct in his dissertation. The committee did find "technical weaknesses" in Steinmeier's citations, but said they were not severe enough to consider revoking his degree.


title: Frank-Walter Steinmeier

text: In April 2022, Steinmeier abandoned plans to visit Kyiv after admitting he would not be welcome in Ukraine in what was seen as a serious snub for one of Germany’s senior politicians. At the time, German news media cited Ukrainian officials as saying that the Ukrainian president Volodymyr Zelensky would refuse to meet Steinmeier if he came to Kyiv. Ukraine had previously criticized Steinmeier for his connections to Russia and his role in strengthening German-Russian relations.


title: Frank-Walter Steinmeier

text: On 25 October 2022, Steinmeier made an official visit to Ukraine, after a scheduled visit on 20 October was cancelled for security reasons due to a wave of cruise missile and drone attacks across Ukraine.


title: Wile E. Coyote and the Road Runner

text: Wile E. Coyote and the Road Runner are a duo of cartoon characters from the "Looney Tunes" and "Merrie Melodies" series of animated cartoons, first appearing in 1949 in the theatrical cartoon short "Fast and Furry-ous". In each episode, the cunning, devious and constantly hungry coyote repeatedly attempts to catch and subsequently eat the Road Runner, but is successful in catching the Road Runner (but not eating it) on only extremely rare occasions. Instead of his animal instincts, the coyote uses absurdly complex contraptions (generally in the manner of Rube Goldberg) to try to catch his prey, which comically backfire, with the coyote often getting injured in slapstick fashion. Many of the items for these contrivances are mail-ordered from a variety of companies implied to be part of the Acme Corporation.


title: Wile E. Coyote and the Road Runner

text: One running gag involves the coyote trying, in vain, to shield himself with a little parasol against a great falling boulder that is about to crush him. Another involves him falling from high cliffs, after momentarily being suspended in midair—as if the fall is delayed until he realizes that there is nothing below him. The rest of the scene, shot from a bird's-eye view, shows him falling into a canyon so deep that his figure is eventually lost to sight, with only a small puff of dust indicating his impact. The coyote is notably a brilliant artist, capable of quickly painting incredibly lifelike renderings of such things as tunnels and roadside scenes, in further (and equally futile) attempts to deceive the bird.


title: Wile E. Coyote and the Road Runner

text: The characters were created for Warner Bros. in 1948 by animation director Chuck Jones and writer Michael Maltese, with Maltese also setting the template for their adventures. The characters star in a long-running series of theatrical cartoon shorts (the first 16 of which were written by Maltese) and occasional made-for-television cartoons. Originally meant to parody chase-cartoon characters like "Tom and Jerry", they became popular in their own right.


title: Wile E. Coyote and the Road Runner

text: The coyote appears separately as an occasional antagonist of Bugs Bunny in five shorts from 1952 to 1963: "", "To Hare Is Human", "Rabbit's Feat", "Compressed Hare", and "Hare-Breadth Hurry". While he is generally silent in the Wile E. Coyote – Road Runner shorts, he speaks with a refined accent in these solo outings (except for "Hare-Breadth Hurry"), beginning with 1952's "", introducing himself as "Wile E. Coyote, Genius", voiced by Mel Blanc. Wile E. Coyote additionally speaks in the 1965 short "Zip Zip Hooray!", where he explains his desire to eat the Road Runner. The Road Runner vocalizes only with his signature "beep, beep" sound, recorded by Paul Julian and an accompanying "popping-cork" tongue sound.


title: Wile E. Coyote and the Road Runner

text: By 2020, 50 cartoons had been made featuring the characters (including the four CGI shorts), the majority by creator Chuck Jones.


title: Wile E. Coyote and the Road Runner

text: Jones based the coyote on Mark Twain's book "Roughing It", in which Twain described the coyote as "a long, slim, sick and sorry-looking skeleton" that is "a living, breathing allegory of Want. He is "always" hungry." Jones said he created the Wile E. Coyote-Road Runner cartoons as a parody of traditional "cat and mouse" cartoons such as MGM's "Tom and Jerry". Jones modelled the coyote's appearance on fellow animator Ken Harris.


title: Wile E. Coyote and the Road Runner

text: The coyote's name of Wile E. is a pun of the word "wily." The "E" stands for "Ethelbert" in one issue of a Looney Tunes comic book. The coyote's surname is routinely pronounced with a long "e" ( ), but in one cartoon short, "To Hare Is Human", Wile E. is heard pronouncing it with a diphthong ( ). Early model sheets for the character prior to his initial appearance (in "Fast and Furry-ous") identified him as "Don Coyote", a pun on Don Quixote.


title: Wile E. Coyote and the Road Runner

text: The Road Runner's "beep, beep sound" was inspired by background artist Paul Julian's imitation of a car horn. Julian voiced the various recordings of the phrase used throughout the Road Runner cartoons, although on-screen he was uncredited for his work. According to animation historian Michael Barrier, Julian's preferred spelling of the sound effect was either "hmeep hmeep" or "mweep, mweep".


title: Wile E. Coyote and the Road Runner

text: The desert scenery in the first three Road Runner cartoons, "Fast and Furry-ous" (1949), "Beep, Beep" (1952), and "Going! Going! Gosh!" (also 1952), was designed by Robert Gribbroek and was quite realistic. In most later cartoons, the scenery was designed by Maurice Noble and was far more abstract.


title: Wile E. Coyote and the Road Runner

text: Wile E. Coyote often obtains various complex and ludicrous devices from a mail-order company, the fictitious Acme Corporation, which he hopes will help him catch the Road Runner. The devices invariably fail in improbable and spectacular fashion.


title: Wile E. Coyote and the Road Runner

text: In August, September and October 1982, the "National Lampoon" published a three-part series chronicling the lawsuit Wile E. filed against the Acme Corporation over the faulty items they sold him in his pursuit of the Road Runner. Even though the Road Runner appeared as a witness for the plaintiff, the coyote still lost the suit.


title: Wile E. Coyote and the Road Runner

text: In his book "Chuck Amuck: The Life and Times of an Animated Cartoonist", Chuck Jones claimed that he and the artists behind the Road Runner and Wile E. Coyote cartoons adhered to some simple but strict rules:


title: Wile E. Coyote and the Road Runner

text: These rules were not always followed, and in an interview years after the series was made, principal writer of the original 16 episodes Michael Maltese stated he had never heard of these or any "rules" and dismissed them as "post production observation".


title: Wile E. Coyote and the Road Runner

text: As in other cartoons, the Road Runner and the coyote follow certain laws of cartoon physics, peculiar to an animation universe. Some examples:


title: Wile E. Coyote and the Road Runner

text: Both animals were typically introduced in a similar fashion; the action would slow to a halt, and a caption would appear with both their common name and a mock genus/species name in pseudo-Latin (for example, in "Zoom at the Top", the Road Runner was classified as "Disappearialis Quickius", while the coyote was identified as "Overconfidentii Vulgaris").


title: Wile E. Coyote and the Road Runner

text: The original Chuck Jones productions ended in 1963 after Jack L. Warner closed the Warner Bros. animation studio. "War and Pieces", the last Wile E. Coyote/Road Runner short directed by Jones, was released on June 6, 1964. By that time, David H. DePatie and director Friz Freleng had formed DePatie–Freleng Enterprises, moved into the facility just emptied by Warner, and signed a license with Warner Bros. to produce cartoons for the big studio to distribute.


title: Wile E. Coyote and the Road Runner

text: Their first cartoon to feature the Road Runner was "The Wild Chase", directed by Freleng in 1965. The premise was a race between the bird and "the fastest mouse in all Mexico," Speedy Gonzales, with the coyote and Sylvester the Cat each trying to make a meal out of their respective usual targets. Much of the material was animation rotoscoped from earlier Road Runner and Speedy Gonzales shorts, with the other characters added in.


title: Wile E. Coyote and the Road Runner

text: In total, DePatie-Freleng produced 14 "Road Runner" cartoons, two of which were directed by Robert McKimson ("Rushing Roulette" (1965) and "Sugar and Spies" (1966)). Eleven of these shorts, directed by Rudy Larriva (often referred to as the "Larriva Eleven"), were subcontracted to Format Films and suffered from severe budget cuts; due to a significant drop in the number of frames used per second in animation, the "Larriva Eleven" were somewhat cheap-looking and jerky. The music was also of poorer quality than the older features; this was a by-product of music director Bill Lava (who had replaced the recently deceased Milt Franklyn three years prior) being relegated to the use of pre-composed music cues - due to the previously mentioned budget cuts - rather than a proper score, as heard with "The Wild Chase", "Rushing Roulette", and "Run Run, Sweet Road Runner" (the third being the only one of the "Larriva Eleven" to have a proper score). These 11 shorts have been considered inferior to the other Golden Age shorts, garnering mixed to poor reviews from critics. In "Of Mice and Magic", Leonard Maltin calls the series "witless in every sense of the word." In addition, except for the planet Earth scene at the tail end of "Highway Runnery", there was only one clip of the coyote's fall to the ground, used over and over again. Jones' previously described "laws" for the characters were not followed with any significant fidelity, nor were Latin phrases used when introducing the characters.


title: Wile E. Coyote and the Road Runner

text: In another series of Warner Bros. "Looney Tunes" cartoons, Chuck Jones used the character design (model sheets and personality) of Wile E. Coyote as "Ralph Wolf". In this series, Ralph continually attempts to steal sheep from a flock being guarded by the eternally vigilant Sam Sheepdog. As with the Road Runner and Wile E. Coyote series, Ralph Wolf uses all sorts of wild inventions and schemes to steal the sheep, but he is continually foiled by the sheepdog. In a move seen by many as a self-referential gag, Ralph Wolf continually tries to steal the sheep not because he is a fanatic (as Wile E. Coyote was), but because it is his job. In every cartoon, he and Sam Sheepdog punch a timeclock and exchange pleasantries, go to work, stop what they are doing to take a lunch break, go back to work and pick up right where they left off, and clock out to go home for the day and exchange pleasantries again, all according to a factory-like blowing whistle. The most obvious difference between the coyote and the wolf, aside from their locales, is that Wile E. has a black nose and Ralph has a red nose.


title: Wile E. Coyote and the Road Runner

text: Wile E. Coyote was called Kelsey Coyote in his comic book debut, a Henery Hawk story in "Looney Tunes and Merrie Melodies" #91 (May 1949). He only made a couple of other appearances at this time and did not have his official name yet, as it was not used until 1952 (in "", his second appearance).


title: Wile E. Coyote and the Road Runner

text: The first appearance of the Road Runner in a comic book was in "Bugs Bunny Vacation Funnies" #8 (August 1958) published by Dell Comics. The feature is titled "Beep Beep the Road Runner" and the story "Desert Dessert". It presents itself as the first meeting between Beep Beep and Wile E. (whose mailbox reads "Wile E. Coyote, Inventor and Genius"), and introduces the Road Runner's wife, Matilda, and their three newly hatched sons (though Matilda soon disappeared from the comics). This story established the convention that the Road Runner family talked in rhyme, a convention that also appeared in early children's book adaptations of the cartoons.


title: Wile E. Coyote and the Road Runner

text: Dell initially published a dedicated "Beep Beep the Road Runner" comic as part of "Four Color Comics" #918, 1008, and 1046 before launching a separate series for the character numbered #4–14 (1960–1962), with the three try-out issues counted as the first three numbers. After a hiatus, Gold Key Comics took over the character with issues #1–88 (1966–1984). During the 1960s, the artwork was done by Pete Alvarado and Phil DeLara; from 1966 to 1969, the Gold Key issues consisted of Dell reprints. Afterward, new stories began to appear, initially drawn by Alvarado and De Lara before Jack Manning became the main artist for the title. New and reprinted Beep Beep stories also appeared in "Golden Comics Digest" and Gold Key's revival of "Looney Tunes" in the 1970s. During this period, Wile E.'s middle name was revealed to be "Ethelbert" in the story "The Greatest of E's" in issue #53 (cover-dated September 1975) of Gold Key Comics' licensed comic book "Beep Beep the Road Runner".


title: Wile E. Coyote and the Road Runner

text: The Road Runner and Wile E. Coyote also make appearances in the DC Comics "Looney Tunes" title. Wile E. was able to speak in some of his appearances in the DC comics.


title: Wile E. Coyote and the Road Runner

text: In 2017, DC Comics featured a "Looney Tunes" and DC Comics crossovers that reimagined the characters in a darker style. The Road Runner and Wile E. Coyote had a crossover with the intergalactic bounty hunter Lobo in "Lobo/Road Runner Special" #1. In this version, the Road Runner, Wile E., and other Looney Tunes characters are reimagined as standard animals who were experimented upon with alien DNA at Acme to transform them into their cartoon forms. In the back-up story, done in more traditional cartoon style, Lobo tries to hunt down the Road Runner, but is limited by Bugs to be more kid-friendly in his language and approach.


title: Wile E. Coyote and the Road Runner

text: The Road Runner and the coyote appeared on Saturday mornings as the stars of their own TV series, "The Road Runner Show", from September 1966 to September 1968, on CBS. At this time it was merged with "The Bugs Bunny Show" to become "The Bugs Bunny and Road Runner Show", running from 1968 to 1985. The show was later seen on ABC until 2000, and on Global until 2001.


title: Wile E. Coyote and the Road Runner

text: In the 1970s, Chuck Jones directed some Wile E. Coyote/Road Runner short films for the educational children's TV series "The Electric Company." These short cartoons used the coyote and the Road Runner to display words for children to read.


title: Wile E. Coyote and the Road Runner

text: In 1979, "Freeze Frame", in which Jones moved the chase from the desert to snow-covered mountains, was seen as part of "Bugs Bunny's Looney Christmas Tales".


title: Wile E. Coyote and the Road Runner

text: At the end of Bugs Bunny's "Portrait of the Artist as a Young Bunny" (the initial sequence of Chuck Jones' TV special "Bugs Bunny's Bustin' Out All Over"), Bugs mentions to the audience that he and Elmer may have been the first pair of characters to have chase scenes in these cartoons, but then a pint-sized baby Wile E. Coyote (wearing a diaper and holding a small knife and fork) runs right in front of Bugs, chasing a gold-colored, mostly unhatched (except for the tail, which is sticking out) Road Runner egg, which is running rapidly while some high-pitched "Beep, beep" noises can be heard. This was followed by the full-fledged Road Runner/Wile E. Coyote short "Soup or Sonic". Earlier in that story, while kid Elmer was falling from a cliff, Wile E. Coyote's adult self tells him to move over and leave falling to people who know how to do it and then he falls, followed by Elmer.


title: Wile E. Coyote and the Road Runner

text: In the 1980s, ABC began showing many Warner Bros. shorts, but in highly edited form. Many scenes integral to the stories were taken out, including scenes in which Wile E. Coyote landed at the bottom of the canyon after having fallen from a cliff, or had a boulder or anvil actually make contact with him. In almost all WB animated features, scenes where a character's face was burnt and black, some thought resembling blackface, were removed, as were animated characters smoking cigarettes. Some cigar smoking scenes were left in. The unedited versions of these shorts (with the exception of ones with blackface) were not seen again until Cartoon Network, and later Boomerang, began showing them again in the 1990s and early 2000s. Since the release of the WB library of cartoons on DVD, the cartoons gradually disappeared from television, presumably to increase sales of the DVDs. However, Cartoon Network began to air them again in 2011, coinciding with the premiere of "The Looney Tunes Show" (2011), and the shorts were afterwards moved to Boomerang, where they have remained to this day.


title: Wile E. Coyote and the Road Runner

text: Wile E. Coyote and the Road Runner appeared in several episodes of "Tiny Toon Adventures". In this series, Wile E. (voiced in the Jim Reardon episode "Piece of Mind" by Joe Alaskey) was the dean of Acme Looniversity and the mentor of Calamity Coyote. The Road Runner's protégé in this series was Little Beeper. In the episode "Piece of Mind", Wile E. narrates the life story of Calamity while Calamity is falling from the top of a tall skyscraper. In the direct-to-video film "", the Road Runner finally gets a taste of humiliation by getting run over by a mail truck that "brakes for coyotes."


title: Wile E. Coyote and the Road Runner

text: The two were also seen in cameos in "Animaniacs". They were together in two "Slappy Squirrel" cartoons: "Bumbie's Mom" and "Little Old Slappy from Pasadena". In the latter, the Road Runner gets another taste of humiliation when he is out-run by Slappy's car, and holds up a sign saying "I quit" — immediately afterward, Buttons, who was launched into the air during a previous gag, lands squarely on top of him. Wile E. appears without the bird in a "The Wizard of Oz" parody, dressed in his batsuit from one short, in a twister (tornado) funnel in "Buttons in Ows". Also, in the beginning of one episode, an artist is seen drawing the Road Runner.


title: Wile E. Coyote and the Road Runner

text: In a Cartoon Network TV ad about "The Acme Hour", Wile E. Coyote utilized a pair of jet roller skates to catch the Road Runner and (quite surprisingly) "did not" fail. While he was cooking his prey, it was revealed that the roller skates came from a generic brand. The ad said that other brand is not the same thing.


title: Wile E. Coyote and the Road Runner

text: The Road Runner appears in an episode of the 1991 series "Taz-Mania", in which Taz grabs him by the leg and gets ready to eat him, until the two gators are ready to capture Taz, so he lets the Road Runner go. In another episode of "Taz-Mania", the Road Runner cartoons are parodied, with Taz dressed as the Road Runner and the character Willy Wombat dressed as Wile E. Coyote. Willy tries to catch Taz with Acme Roller Skates but fails, and Taz even says "Beep, beep".


title: Wile E. Coyote and the Road Runner

text: Wile E. and the Road Runner appeared in their toddler versions in "Baby Looney Tunes", but only in songs. However, they both had made a cameo in the episode "Are We There Yet?", where the Road Runner was seen out the window of Floyd's car with Wile E. chasing him.


title: Wile E. Coyote and the Road Runner

text: Wile E. Coyote had a cameo as the true identity of an alien hunter (a parody of "Predator") in the "Duck Dodgers" episode "K-9 Quarry," voiced by Dee Bradley Baker. In that episode, he was hunting Martian Commander X-2 and K-9. He is also temporary as a member of Agent Roboto's Legion of Duck Doom from the previous season in another episode.


title: Wile E. Coyote and the Road Runner

text: In "Loonatics Unleashed", Wile E. Coyote and the Road Runner's 28th century descendants are Tech E. Coyote (voiced by Kevin Michael Richardson) and Rev Runner (voiced by Rob Paulsen). Tech E. Coyote was the tech expert of the Loonatics (influenced by the past cartoons with many of the machines ordered by Wile E. from Acme), and has magnetic hands and the ability to molecularly regenerate himself (influenced by the many times in which Wile E. painfully failed to capture the Road Runner and then was shown to have miraculously recovered). Tech E. Coyote speaks, but does not have a British accent as Wile E. Coyote did. Rev Runner is also able to talk, though extremely rapidly, and can fly without the use of jet packs, which are used by other members of the Loonatics. He also has sonic speed, also a take-off of the Road Runner. The pair get on rather well, despite the number of gadgets Tech designs in order to stop Rev from talking; also they have their moments where they do not get along. When friendship is shown it is often only from Rev to Tech, not the other way around; this could, however, be attributed to the fact that Tech has only the barest minimum of social skills. They are both portrayed as smart, but Tech is the better inventor and at times Rev is shown doing stupid things. References to their ancestors' past are seen in the episode "Family Business" where the other Road Runners are wary of Tech and Tech relives the famous falling gags done in the Wile E. Coyote/Road Runner shorts.


title: Wile E. Coyote and the Road Runner

text: The Road Runner and Wile E. Coyote feature in 3D computer animated cartoons or cartoon animation in the Cartoon Network TV series "The Looney Tunes Show". The CGI shorts were only included in Season 1, but Wile E. and the Road Runner still appeared throughout the series in 2D animation.


title: Wile E. Coyote and the Road Runner

text: Wile E. Coyote also appears in the TV series "Wabbit", voiced by JP Karliak, in a similar vein to his previous pairings with Bugs Bunny. He appears as Bugs' annoying know-it-all neighbor who always uses his inventions to compete with Bugs. The Road Runner began making appearances when the series was renamed "New Looney Tunes" in 2017.


title: Wile E. Coyote and the Road Runner

text: Wile E. Coyote and the Road Runner both appear in their own cartoon shorts in the HBO Max streaming series "Looney Tunes Cartoons".


title: Wile E. Coyote and the Road Runner

text: Wile E. Coyote and the Road Runner make occasional appearances in the preschool educational series "Bugs Bunny Builders". Wile E. (voiced by Keith Ferguson) often helps the Looney Builders out with their plans, often using some of his inventions. In the episode "Looney Science", Wile E. has the Looney Builders build him a science museum to show off his inventions, but the Road Runner keeps constantly distracting him.


title: Wile E. Coyote and the Road Runner

text: Wile E. Coyote was also in an episode of "Night Court" (Season 7, Episode 22: "Sill Another Day in the Life") in which Judge Harold T. Stone (Harry Anderson) found him guilty of harassment and told him to leave the poor bird alone.


title: Wile E. Coyote and the Road Runner

text: The characters appeared in seven 3-D shorts attached to Warner Bros. features. Three have been screened with features, while the rest serve as segments in season 1 of "The Looney Tunes Show". A short called "Flash in the Pain" was shown on the web in 2014, but was not shown in theaters until 2016, when the movie Storks premiered.


title: Wile E. Coyote and the Road Runner

text: Warner Bros. is developing a live-action/animation hybrid film centered on Wile E. Coyote titled "Coyote vs. Acme", produced by Warner Animation Group, with "The Lego Batman Movie" director Chris McKay on board to produce. The film is said to be based on "The New Yorker" short story "Coyote v. Acme" by author Ian Frazier. Published in 1990, the piece imagined a lawsuit brought about by Wile E. Coyote against the Acme Company who provided him with various devices and tools to aid in his pursuit of the Road Runner. The devices frequently malfunctioned, leading to the humorous failures, injuries, and sight gags the Road Runner cartoons are known for. Jon and Josh Silberman were originally set to write the screenplay. On December 18, 2019, it was reported that Dave Green will direct the project. It was also reported that the project is looking for a new writer, with Jon and Josh Silberman instead co-producing the film alongside McKay; however, by December 2020, McKay departed the project while Jon and Josh Silberman left their roles as producers and resumed their screenwriting roles, with Samy Burch, Jeremy Slater, and James Gunn also writing the film. Gunn will also co-produce the project alongside Chris DeFaria. It was also announced that the film is scheduled to be released on July 21, 2023. In February 2022, it was announced that John Cena would star in the film. In March 2022, Will Forte and Lana Condor were added to the cast.


title: Wile E. Coyote and the Road Runner

text: The voice artist Paul Julian originated the character's voice. Before and after his death, his voice was appearing in various media, for example, in TV series, shorts and video games, such as 2014's "Looney Tunes Dash". In addition, other voice actors have replaced him. These voice actors are:


title: Wile E. Coyote and the Road Runner

text: Wile E. Coyote and the Road Runner have been frequently referenced in popular culture. Some explamples:


title: Wile E. Coyote and the Road Runner

text: There are two scenes in Stanley Kubrick's 1980 adaptation of "The Shining" where Danny Torrance and his mother, Wendy Torrance, are watching the cartoons.


title: Wile E. Coyote and the Road Runner

text: Wile E. Coyote and the Road Runner appeared in the 1988 Touchstone/Amblin film "Who Framed Roger Rabbit." They are first seen silhouetted by the elevator doors in Toontown, and then in full in the ACME Factory during the final scene with other characters.


title: Wile E. Coyote and the Road Runner

text: Wile E. Coyote has appeared twice in "Family Guy": his first episode, "I Never Met the Dead Man", depicts him riding in a car with Peter Griffin; when Peter runs over the Road Runner and asks if he hit "that ostrich", Wile E. tells him to keep going. His second appearance was in "PTV", in which Wile E. attempts to get a refund for a giant-sized slingshot at an ACME retailer where Peter works. The DVD-exclusive episode "Partial Terms of Endearment" features a gag that parodies the Wile E./Road Runner cartoons where Peter lures Lois with free "Grey's Anatomy" DVDs (in the vein of Wile E. luring the Road Runner with free bird seed) and attempts to terminate her pregnancy by firing a boxing glove at her from a crossbow atop a cliff; this fails, and Peter ends up falling off the cliff in Wile E.-fashion.


title: Wile E. Coyote and the Road Runner

text: Wile E. Coyote and the Road Runner appeared in "Seth MacFarlane's Cavalcade of Cartoon Comedy" in the short "Die, Sweet Roadrunner, Die". In this short, Wile E. crushes the Road Runner with a large boulder and eats him, but then struggles to find purpose in life, having not trained for anything else other than chasing the Road Runner. Ultimately, after a short-lived job as a waiter in a local diner, and a suicide attempt (by way of catapulting himself into a mountain at close range), Wile E. finally realizes what he is to do with his life, and reveals he is now an advocate for Christianity.


title: Wile E. Coyote and the Road Runner

text: Both Wile E. Coyote and the Road Runner have appeared in "Robot Chicken" on multiple occasions. One sketch sees Wile E. faking his own suicide and then torching the Road Runner with a flamethrower when he shows up at Wile E.'s "funeral". Another sketch shows Wile E. teaching a college course on how to get away with murder, using the Road Runner's murder as an example; the students trace the mail orders for the ACME products used to commit the murder to Wile E., who is executed by electric chair for the crime. Another sketch sees Wile E. presenting his iconic "fake tunnel" at an art auction, and another reveals why Wile E.'s ACME products always fail - the ACME Corporation is run by multiple Road Runners.


title: Wile E. Coyote and the Road Runner

text: Guitarist Mark Knopfler created a song called "Coyote" in homage to the cartoon shows of Wile E. Coyote and the Road Runner on the 2002 album "The Ragpicker's Dream". The Tom Smith song "Operation: Desert Storm", which won a Pegasus award for Best Fool Song in 1999, is about the different crazy ways the coyote's plans fail.


title: Wile E. Coyote and the Road Runner

text: Dee Snider, lead singer of the glam metal band Twisted Sister stated in his Congressional testimony before the PRMC hearings on adding Parental Advisory labels in music and music videos, that the music video for the band's signature song "We're Not Gonna Take It" was based heavily on the cartoon.


title: Wile E. Coyote and the Road Runner

text: Humorist Ian Frazier created the mock-legal prose piece "Coyote v. Acme", which is included in a book of the same name.


title: Wile E. Coyote and the Road Runner

text: During a scene in "", the "Drawn Together" cast accidentally run over and kill the Road Runner with Foxxy Love's van. Upon noticing this, Wile E. Coyote runs up to the Road Runner's corpse and declares "Without you, my life really has no meaning", before shooting himself with a "Bang!" flag gun.


title: Melissa George

text: Melissa George (born 6 August 1976) is an Australian actress and entrepreneur. A former national artistic rollerskating champion and model, George began her acting career playing Angel Parrish in the Australian soap opera Home and Away (1993–1996). After moving to the United States, George made her feature film debut in "Dark City" (1998). She later had supporting roles in Steven Soderbergh's "The Limey" (1999), David Lynch's "Mulholland Drive" (2001), "Sugar & Spice" (2001), and "Down with Love" (2003).


title: Melissa George

text: George made the transition to leading roles when she appeared as Kathy Lutz in the 2005 remake of "The Amityville Horror". She followed this with a succession of films in the thriller and horror genres, such as "Derailed" (2005), "Turistas" (2006), "WΔZ" (2007), "30 Days of Night" (2007), "Triangle" (2009), "A Lonely Place to Die" (2011), and "Felony" (2013).