20050455
Clique-Width for 4-Vertex Forbidden Subgraphs
Clique-width of graphs is a major new concept with respect to efficiency of graph algorithms. The notion of clique-width extends the one of treewidth, since bounded treewidth implies bounded clique-width. We give a complete classification of all graph classes defined by forbidden induced subgraphs of at most four vertices with respect to bounded or unbounded clique-width.
17560850
Clique-Width for Four-Vertex Forbidden Subgraphs
Clique-width of graphs is a major new concept with respect to efficiency of graph algorithms. The notion of clique-width extends the one of treewidth, since bounded treewidth implies bounded clique-width. We give a complete classification of all graph classes defined by forbidden induced subgraphs of at most four vertices with respect to bounded or unbounded clique-width.
14472583
An exercise in structural congruence
Milner's structural congruence is decidable for the pi-calculus without restriction, in exponential space.
5981521
Nested Pebbles and Transitive Closure
First-order logic with k-ary deterministic transitive closure has the same power as two-way k-head deterministic automata that use a finite set of nested pebbles. This result is valid for strings, ranked trees, and in general for families of graphs having a fixed automaton that can be used to traverse the nodes of each of the graphs in the family. Other examples of such families are grids, toruses, and rectangular mazes.
27165586
A new natural structural congruence in the pi-calculus with replication
Abstract.In the $\pi$-calculus with replication, a new structural congruence called “middle” congruence is investigated: a notion of structural equivalence of processes in which replication of a process is viewed as a potential rather than an actual infinite number of copies of the process, in the sense that copies are spawned at need rather than produced all at once. It is slightly weaker than standard congruence (which is also of the potential type) but stronger than the extended congruence investigated before by the authors (which is of the actual type). It is shown that middle congruence has the same desirable properties as extended congruence: it is decidable and it has a concrete multiset semantics. Thus, these properties do not depend on the distinction between potential and actual replication.
15175574
Branching synchronization grammars with nested tables
A generalization of ET0L systems is introduced: grammars with branching synchronization and nested tables. The main result is that branching synchronization grammars with tables of nesting depth n have the same string- and tree-generating power as n-fold compositions of top-down tree transducers. Based on this it is shown, e.g., that the family of generated string languages is a full principal AFL for each n.
34994233
Iterated deterministic substitution
SummaryDeterministic substitution of languages means substituting the same word (from a given language) for all occurrences of a symbol. For an arbitrary family K of languages the notion of deterministic K-iteration grammar is introduced, which is essentially the iteration of a finite number of deterministic substitutions of languages from K. The families of languages generated by these grammars are investigated.
9686977
A Temporal Model Theory for Default Logic
By explicitly identifying the temporal aspect of a default rule as it is used in a reasoning process, it is argued that a natural semantic theory of Reiter's default logic is a temporal one. To be able to accommodate the lack of complete knowledge at any point in time, the temporal models should be partial models. A temporal partial logic is introduced, and it is shown that this logic can provide semantics for Reiter's default logic.
41515310
Minimal Temporal Epistemic Logic
15030192
Nonmonotonic reasoning with multiple belief sets
In complex reasoning tasks it is often the case that there is no single, correct set of conclusions given some initial information. Instead, there may be several such conclusion sets, which we will call belief sets. In the present paper we introduce nonmonotonic belief set operators and selection operators to formalize and to analyze structural aspects of reasoning with multiple belief sets. We define and investigate formal properties of belief set operators as absorption, congruence, supradeductivity and weak belief monotony. Furthermore, it is shown that for each belief set operator satisfying strong belief cumulativity there exists a largest monotonic logic underlying it, thus generalizing a result for nonmonotonic inference operations. Finally, we study abstract properties of selection operators connected to belief set operators, which are used to choose some of the possible belief sets.
17644062
Specification of nonmonotonic reasoning
ABSTRACT Two levels of description of nonmonotonic reasoning are distinguished. For these levels semantical formalizations are given. The first level is defined semantically by the notion of belief state frame, the second level by the notion of reasoning frame. We introduce two specification languages to describe nonmonotonic reasoning at each of the levels: (1) a specification language for level 1, with formal semantics based on belief state frames, (2) a fragment of infinitary temporal logic as a general specification language for level 2, with formal semantics based on reasoning frames. In our framework every level 2 description can be abstracted to level 1, and for every level 1 description there are level 2 descriptions which are a specialization of it.