29040872
A Variant to Turing's Theory of Computing Machines
The principal purpose of this paper is to offer a theory which is closely related to Turing's [1] but is more economical in the basic operations. I t will be proved that a theoretically simple basic machine can be imagined and specified such tha t all partial recursive functions (and hence all solvable computation problems) can be computed by it and tha t only four basic types of instruction are employed for the programs: shift left one space, shift right one space, mark a blank space, conditional transfer. In particular, erasing is dispensable, one symbol for marking is sufficient, and one kind of transfer is enough. The reduction is somewhat similar to the realization of, for instance, the definability of conjunction and implication in terms of negation and disjunction, or of the definability of all these in terms of Sheffer's stroke function. As a result, i t becomes less direct to prove that certain things can be done by the machines, but a little easier to prove that certain things cannot be done. This serf-contained theory will b e presented, as far as possible, in a language which is familiar to those who are engaged in the use and construction of largescale computers. Turing's theory of computable functions antedated but has not much influenced the extensive actual construction of digital computers. These two aspects of theory and practice have been developed almost entirely independently of each other. The main reason is undoubtedly that logicians are interested in questions radically different from those with which the applied mathematicians and electrical engineers are primarily concerned. I t cannot, however, fail to strike one as rather strange that often the same concepts are expressed by very different terms in the two developments. One is even inclined to ask whether a rapprochement might not produce some good effect. This paper wiU, it is believed, be of use to those who wish to compare and connect the two approaches. Extensive use of Turing [1] and Kleene [2] (Chapter XI I I ) will be made, although the exposition is sufficient in itself.
26896458
The Axiomatization of Arithmetic
34944417
Logic of Many-Sorted Theories
Certain axiomatic systems involve more than one category of fundamental objects; for example, points, lines, and planes in geometry; individuals, classes of individuals, etc. in the theory of types or in predicate calculi of orders higher than one. It is natural to use variables of different kinds with their ranges respectively restricted to different categories of objects, and to assume as substructure the usual quantification theory (the restricted predicate calculus) for each of the various kinds of variables together with the usual theory of truth functions for the formulas of the system. An axiomatic theory set up in this manner will be called many-sorted. We shall refer to the theory of truth functions and quantifiers in it as its (many-sorted) elementary logic, and call the primitive symbols and axioms (including axiom schemata) the proper primitive symbols and proper axioms of the system. Our purpose in this paper is to investigate the many-sorted systems and their elementary logics. Among the proper primitive symbols of a many-sorted system T n ( n = 2, …, ω ) there may be included symbols of some or all of the following kinds: (1) predicates denoting the properties and relations treated in the system; (2) functors denoting the functions treated in the system; (3) constant names for certain objects of the system. We may either take as primitive or define a predicate denoting the identity relation in T n .
21405683
Set-Theoretical Basis for Real Numbers
twenty axioms used by Tarski which are sufficient for the arithmetic of real numbers and are to the effect that real numbers form a complete ordered field.2 Indeed, we cannot prove in L all Tarski's twenty axioms in their full generality. One of them, stating in effect that every bounded class of real numbers possesses a least upper bound, can only be proved as a metatheorem which states that every bounded nameable class of real numbers possesses a least upper bound. However, all the other nineteen axioms can be proved in L without any modification. This result may be of some interest because the axioms of L are considerably weaker than those commonly employed for the same purpose. In L variables need to take as values only classes each of whose members has no more than two members. In other words, only classes each with no more than two members are to be elements. On the other hand, it is usual to assume for the purpose of natural arithmetic that all finite classes are elements, and, for the purpose of real arithmetic, that all enumerable classes are elements. 2. The system L. In developing L, elementary logic (viz., the theory of truth functions and quantifiers) is assumed from the beginning. The single additional primitive is the two place predicate e with which we can generate formulas of L from variables and logical operators in the usual manner. The usual definitions (e.g., D9-D35 of [21) of the theory of classes and relations are assumed. In particular, let tx denote the unit class of x, x u y denote the sum class of x and y, and V denote the class of all elements. The axioms of L are given by the following three statements: Mi. tx U by f V. M2. x = y D . x e z D y e z. M3. If q is any formula of L in which y is not free, then . (3y)(x)(x e yW
33404030
Some Facts About Kurt Godel
8390786
A modular NFA architecture for regular expression matching
We propose a non-deterministic finite automata (NFA) based architecture for regexp scanners on FPGA, called CES: the Character Class with Constraint Repetition (CCR) based regExp Scanner. CES is designed to realize a new MIN-MAX counting algorithm, which can solve both the character class ambiguity problem and the overlapped matching problem. CES also supports non-regular Perl grammars such as zero-width pattern and back-reference. We propose a CCR-syntax tree and its parsing scheme to map a Perl or POSIX regexp rule to a CES topology. The interconnection patterns, and operational parameters of CCR modules (CCRM), which are the building blocks of CES, can be easily configured by regular memory writes when regexp rules change, without re-synthesis of low-level logic.
 For implementation, character classes of CCRs are stored in Block RAMs. The MIN-MAX algorithm uses two counters MIN and MAX to resolve the character class ambiguity problem. Two checkpoint counters are employed to implement overlapped matching detection. CES topologies optimized for different types of rules can run in different Partial Reconfigurable Regions (PRR), and can be swapped on the fly by a PRR controller. We developed a tool chain to automate the CES implementation to a Virtex 5 LX110T device. This device can host up to 3000 CCRMs, and run at an estimated throughput of 1.996 Gbps in simulation, and 863 Mbps between a PC and the Virtex 5 board in real tests. The Snort and SpamAssassin rule sets can be parsed and mapped in milliseconds. Once a base CES architecture is synthesized, the physical reconfiguration of a CES on the Virtex 5 LX110T chip can be done in less than a second.
7290502
Towards automatic generation of vulnerability-based signatures
In this paper we explore the problem of creating vulnerability signatures. A vulnerability signature matches all exploits of a given vulnerability, even polymorphic or metamorphic variants. Our work departs from previous approaches by focusing on the semantics of the program and vulnerability exercised by a sample exploit instead of the semantics or syntax of the exploit itself. We show the semantics of a vulnerability define a language which contains all and only those inputs that exploit the vulnerability. A vulnerability signature is a representation (e.g., a regular expression) of the vulnerability language. Unlike exploit-based signatures whose error rate can only be empirically measured for known test cases, the quality of a vulnerability signature can be formally quantified for all possible inputs. We provide a formal definition of a vulnerability signature and investigate the computational complexity of creating and matching vulnerability signatures. We also systematically explore the design space of vulnerability signatures. We identify three central issues in vulnerability-signature creation: how a vulnerability signature represents the set of inputs that may exercise a vulnerability, the vulnerability coverage (i.e., number of vulnerable program paths) that is subject to our analysis during signature creation, and how a vulnerability signature is then created for a given representation and coverage. We propose new data-flow analysis and novel adoption of existing techniques such as constraint solving for automatically generating vulnerability signatures. We have built a prototype system to test our techniques. Our experiments show that we can automatically generate a vulnerability signature using a single exploit which is of much higher quality than previous exploit-based signatures. In addition, our techniques have several other security applications, and thus may be of independent interest
15663663
Kernel based articulated object tracking with scale adaptation and model update
Kernel based object tracking (KBOT) is one of the most popular and effective techniques for tracking task. However the constancy of the target model and unsound scale adaptation method are two main limitations. In this paper, we present a kernel based approach incorporated with scale estimation and target model update for articulated object tracking task. After predicating the object center with scale fixed KBOT, we extend scale selection theory to estimate the local optimal object scale. Once the object scale has been estimated, a kernel density estimation based strategy is developed to update the target model. Experimental results show that our approach is superior to traditional KBOT in the following two aspects: 1) it is less affected by the object scale change; 2) it is less prone to appearance variation.
940637
Apply ant colony optimization to Tetris
Tetris is a falling block game where the player's objective is to arrange a sequence of different shaped tetrominoes smoothly in order to survive. In the intelligence games, agent imitates the real player and chooses the best move based on a linear value function. In this paper, we apply Ant Colony Optimization (ACO) method to learn the weights of the function, trying to search an optimal weight-path in the weight graph. We use dynamic heuristic to prevent premature convergence to local optima. Our experimental result is better than most of traditional reinforcement learning methods.
6016307
Research and Implementation of Knowledge-Enhanced Information Services
Information isolation has been identified as a big challenge in IT Service Management (ITSM). Existing ITSM practices mostly rely on configuration information and are geared towards individual applications and processes. However, information available in complicated IT infrastructure goes beyond data from the configuration management domain. How to efficiently extract and integrate the hidden knowledge from a wide variety of information sources is a major pain point for ITSM. In this paper, a threading strategy (TS) with KPI mark and knowledge-enhanced information services is proposed to improve ITSM quality. The essential contribution of this work is to organize the highly complex IT service information with KPI mark and to build a knowledge repository for accumulateing and reusing experts' knowledge. In addition, a prototype called BIANCHIN is implemented to explore this knowledge-enhanced information services framework. Finally, a real business application of Cisco VoIP system is used as a case study for evaluating the effectiveness and efficiency of the knowledge-enhanced information services framework.