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Algorithms for the Satisfiability (SAT) Problem: A Survey
 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1996
"... . 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, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, compute ..."
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Cited by 127 (3 self)
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. 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, computeraided 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...
Ordered Semantic HyperLinking
, 1994
"... We propose a method for combining the clause linking theorem proving method with theorem proving methods based on orderings. This may be useful for incorporating termrewriting based approaches into clause linking. In this way, some of the propositional inefficiencies of orderingbased approaches ..."
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Cited by 24 (3 self)
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We propose a method for combining the clause linking theorem proving method with theorem proving methods based on orderings. This may be useful for incorporating termrewriting based approaches into clause linking. In this way, some of the propositional inefficiencies of orderingbased approaches may be overcome, while at the same time incorporating the advantages of ordering methods into clause linking. The combination also provides a natural way to combine resolution on nonground clauses, with the clause linking method, which is essentially a ground method. We describe the method, prove completeness, and show that the enumeration part of clause linking with semantics can be reduced to polynomial time in certain cases. We analyze the complexity of the proposed method, and also give some plausibility arguments concerning its expected performance. 1 Introduction There are at least two basic approaches to the study of automated deduction. One approach concentrates on solving...
Knowledge Representation and Classical Logic
"... Mathematical logicians had developed the art of formalizing declarative knowledge long before the advent of the computer age. But they were interested primarily in formalizing mathematics. Because of the important role of nonmathematical knowledge in AI, their emphasis was too narrow from the perspe ..."
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Cited by 10 (4 self)
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Mathematical logicians had developed the art of formalizing declarative knowledge long before the advent of the computer age. But they were interested primarily in formalizing mathematics. Because of the important role of nonmathematical knowledge in AI, their emphasis was too narrow from the perspective of knowledge representation, their formal languages were not sufficiently expressive. On the other hand, most logicians were not concerned about the possibility of automated reasoning; from the perspective of knowledge representation, they were often too generous in the choice of syntactic constructs. In spite of these differences, classical mathematical logic has exerted significant influence on knowledge representation research, and it is appropriate to begin this handbook with a discussion of the relationship between these fields. The language of classical logic that is most widely used in the theory of knowledge representation is the language of firstorder (predicate) formulas. These are the formulas that John McCarthy proposed to use for representing declarative knowledge in his advice taker paper [176], and Alan Robinson proposed to prove automatically using resolution [236]. Propositional logic is, of course, the most important subset of firstorder logic; recent
Convergence Properties of Optimization Algorithms for the Satisfiability (SAT) Problem
 IEEE Trans. on Computers
, 1996
"... : The satisfiability (SAT) problem is a basic problem in computing theory. Presently, an active area of research on SAT problem is to design efficient optimization algorithms for finding a solution for a satisfiable CNF formula. A new formulation, the Universal SAT problem model, which transforms t ..."
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Cited by 2 (1 self)
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: The satisfiability (SAT) problem is a basic problem in computing theory. Presently, an active area of research on SAT problem is to design efficient optimization algorithms for finding a solution for a satisfiable CNF formula. A new formulation, the Universal SAT problem model, which transforms the SAT problem on Boolean space into an optimization problem on real space has been developed [31, 35, 34, 32]. Many optimization techniques, such as the steepest descent method, Newton's method, and the coordinate descent method, can be used to solve the Universal SAT problem. In this paper, we prove that, when the initial solution is sufficiently close to the optimal solution, the steepest descent method has a linear convergence ratio fi ! 1, Newton's method has a convergence ratio of order two, and the convergence ratio of the steepest descent method is approximately (1 \Gamma fi=m) for the Universal SAT problem with m variables. An algorithm based on the coordinate descent method for the...
Efficient FirstOrder Semantic Deduction Techniques
, 1998
"... Mathematical logic formalizes the process of mathematical reasoning. For centuries, it has been a dream of mathematicians to do mathematical reasoning mechanically. In the TPTP library, one finds thousands of problems from various domains of mathematics such as group theory, number theory, set theor ..."
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Mathematical logic formalizes the process of mathematical reasoning. For centuries, it has been a dream of mathematicians to do mathematical reasoning mechanically. In the TPTP library, one finds thousands of problems from various domains of mathematics such as group theory, number theory, set theory, etc. Many of these problems can now be solved with state of the art automated theorem provers. Theorem proving also has applications in artificial intelligence and formal verification. As a formal method, theorem proving has been used to verify the correctness of various hardware and software designs. In this thesis, we propose a novel firstorder theorem proving strategy  ordered semantic hyper linking (OSHL). OSHL is an instancebased theorem proving strategy. It proves firstorder unsatisfiability by generating instances of firstorder clauses and proving the set of instances to be propositionally unsatisfiable. OSHL can use semantics, i.e. domain information, to guide its search. OS...
The role of heuristics in automated theorem proving – J.A. Robinson’s resolution principle
 Mathware & Soft Computing
, 1996
"... with infinite events and changes, it is impossible one doesn't write, at least one time, Odyssey (J.L. Borges, The Aleph) Abstract The aim of this paper is to show how J.A. Robinson's resolution principle was perceived and discussed in the AI community between the mid sixties and the first seventies ..."
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with infinite events and changes, it is impossible one doesn't write, at least one time, Odyssey (J.L. Borges, The Aleph) Abstract The aim of this paper is to show how J.A. Robinson's resolution principle was perceived and discussed in the AI community between the mid sixties and the first seventies. During this time the so called "heuristic search paradigm " was still influential in the AI community, and both resolution principle and certain resolution based, apparently humanlike, search strategies were matched with those problem solving heuristic procedures which were representative of the AI heuristic search paradigm. 1
An Improved Propositional Approach to FirstOrder Theorem Proving
"... Ordered semantic hyperlinking (OSHL) is a theorem prover for firstorder logic that generates models and uses them to instantiate firstorder clauses to ground clauses, and applies a propositional prover to these ground clauses. OSHLU extends OSHL with rules for unit clauses and with heuristics. ..."
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Ordered semantic hyperlinking (OSHL) is a theorem prover for firstorder logic that generates models and uses them to instantiate firstorder clauses to ground clauses, and applies a propositional prover to these ground clauses. OSHLU extends OSHL with rules for unit clauses and with heuristics. The unit rules in OHSLU are designed to minimize the use of blind instantiation to generate ground instances of input clauses. OSHLU demonstrates significantly improved performance over OSHL on the TPTP problem set, and also performs better than OSHL with semantics and OSHL with replacement rules and definition detection on set theory problems. Despite its propositional approach, OSHLU also obtains more than half of the problems that Otter solves with the auto flag on the TPTP problem set in 30 seconds, and has comparable or superior performance on several groups of TPTP problems. This is especially interesting because OSHLU has no special rules for equality axioms. This is the first time, to our knowledge, that a propositional style prover, not performing unifications between non ground literals, has demonstrated performance comparable to that of a resolution prover on groups of TPTP problems that are not nearpropositional in structure. These results suggest that a propositional prover may be superior on some classes of problems, particularly nonHorn problems, to provers based on the resolutionunification and model elimination paradigms.