The Search Efficiency Of Theorem Proving Strategies
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The Efficiency of Theorem Proving Strategies
Author: David A. Plaisted
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-11-11
This is the second and slightly revised edition of this book. A few errors have been fixed, and some references to related work have been added. I thank the readers for their comments on the first edition. We analyze the search efficiency of a number of common refutational theorem proving strategies on propositional and near-propositional prob lems. Search efficiency is concerned with the total number of proofs and partial proofs generated, rather than with the sizes of the proofs. We show that most common strategies produce search spaces of expo nential size even on simple sets of clauses, or else are not sensitive to the goal. However, clause linking, which uses a reduction to proposi tional calculus, has behavior that is more favorable in some respects, a property that it shares with methods that cache subgoals. A strat egy which is of interest for term-rewriting based theorem proving is the A-ordering strategy, and we discuss it in some detail. We show some advantages of A-ordering over other strategies, which may help to explain its efficiency in practice. We also point out some of its com binatorial inefficiencies, especially in relation to goal-sensitivity and irrelevant clauses. In addition, SLD-resolution, which is of importance for Prolog implementation, has combinatorial inefficiencies; this may suggest basing Prolog implementations on a different theorem proving strategy. We also develop techniques for studying the asymptotic complexity of first-order theorem provers. This permits an analytic comparison of the worst-case performances of various theorem proving methods.
Satisfiability Problem: Theory and Applications
The satisfiability (SAT) problem is central in mathematical logic, computing theory, and many industrial applications. There has been a strong relationship between the theory, the algorithms and the applications of the SAT problem. This book aims to bring together work by the best theorists, algorithmists, and practitioners working on the sat problem and on industrial applications, as well as to enhance the interaction between the three research groups. The book features the applications of theoretical/algorithmic results to practical problems and presents practical examples for theoretical/algorithmic study. Major topics covered in the book include practical and industial SAT problems and benchmarks, significant case studies and applications of the SAT problem and SAT algorithms, new algorithms and improved techniques for satisfiability testing, specific data structures and implementation details of the SAT algorithms, and the theoretical study of the SAT problem and SAT algorithms.
Automated Deduction, Cade-12.
Author: Alan Bundy
language: en
Publisher: Springer Science & Business Media
Release Date: 1994-06-08
This volume contains the reviewed papers presented at the 12th International Conference on Automated Deduction (CADE-12) held at Nancy, France in June/July 1994. The 67 papers presented were selected from 177 submissions and document many of the most important research results in automated deduction since CADE-11 was held in June 1992. The volume is organized in chapters on heuristics, resolution systems, induction, controlling resolutions, ATP problems, unification, LP applications, special-purpose provers, rewrite rule termination, ATP efficiency, AC unification, higher-order theorem proving, natural systems, problem sets, and system descriptions.