Term Rewriting Systems play an important role in various areas, such as abstract data type specifications, implementations of functional programming languages and automated deduction. In this chapter we introduce several of the basic comcepts and facts for TRS's. Specifically, we discuss Abstract Reduction Systems

Abstract not found

We present techniques to prove termination and innermost termination of term rewriting systems automatically. In contrast to previous approaches, we do not compare left- and right-hand sides of rewrite rules, but introduce the notion of dependency pairs to compare left-hand sides with special subterms of the right-hand sides. This results in a technique which allows to apply existing methods for automated termination proofs to term rewriting systems where they failed up to now. In particular, there are numerous term rewriting systems where a direct termination proof with simplification orderings is not possible, but in combination with our technique, well-known simplification orderings (such as the recursive path ordering, polynomial orderings, or the Knuth-Bendix ordering) can now be used to prove termination automatically. Unlike previous methods, our technique for proving innermost termination automatically can also be applied to prove innermost termination of term rewriting systems that are not terminating. Moreover, as innermost termination implies termination for certain classes of term rewriting systems, this technique can also be used for termination proofs of such systems.

... quickly across a wide range of hard SAT problems than any other SAT tester in the literature on comparable platforms. On a Sun SPARCStation 10 running SunOS 4.1.3 U1, POSIT can solve hard random 400-variable 3-SAT problems in about 2 hours on the average. In general, it can solve hard n-variable random 3-SAT problems with search trees of size O(2 n=18:7 ). In addition to justifying these claims, this dissertation describes the most significant achievements of other researchers in this area, and discusses all of the widely known general techniques for speeding up SAT search algorithms. It should be useful to anyone interested in NP-complete problems or combinatorial optimization in general, and it should be particularly useful to researchers in either Artificial Intelligence or Operations Research.

Abstract not found

We present an "unfailing" extension of the standard KnuthBendix completion procedure that is guaranteed to produce a desired canonical system, provided certain conditions are met. Weprove that this unfailing completion method is refutationally complete for theorem proving in equational theories. The method can also be applied to Horn clauses with equality, in which case it corresponds to positive unit resolution plus oriented paramodulation, with unrestricted simplification.

We provide a theoretical basis for studying termination of (general) logic programs with the Prolog selection rule. To this end we study the class of left terminating programs. These are logic programs that terminate with the Prolog selection rule for all ground goals. We offer a characterization of left terminating positive programs by means of the notion of an acceptable program that provides us with a practical method of proving termination. The method is illustrated by giving a simple proof of termination of the quicksort program for the desired class of goals. Then we extend this approach to the class of general logic programs by modifying the concept of acceptability. We prove that acceptable general programs are left terminating. The converse implication does not hold but we show that under the assumption of nonfloundering from ground goals every left terminating general program is acceptable. Finally, we prove that various ways of defining semantics coincide for acceptable gen...

. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computer-aided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...

Abstract not found

CFT is a new constraint system providing records as logical data structure for constraint (logic) programming. It can be seen as a generalization of the rational tree system employed in Prolog II, where finer-grained constraints are used, and where subtrees are identified by keywords rather than by position. CFT is defined by a first-order structure consisting of so-called feature trees. Feature trees generalize the ordinary trees corresponding to first-order terms by having their edges labeled with field names called features. The mathematical semantics given by the feature tree structure is complemented with a logical semantics given by five axiom schemes, which we conjecture to comprise a complete axiomatization of the feature tree structure. We present a decision method for CFT, which decides entailment / disentailment between possibly existentially quantified constraints. Since CFT satisfies the independence property, our decision method can also be employed for checking the sat...