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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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. 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...
Finding Hard Instances of the Satisfiability Problem: A Survey
, 1997
"... . Finding sets of hard instances of propositional satisfiability is of interest for understanding the complexity of SAT, and for experimentally evaluating SAT algorithms. In discussing this we consider the performance of the most popular SAT algorithms on random problems, the theory of average case ..."
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Cited by 128 (1 self)
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. Finding sets of hard instances of propositional satisfiability is of interest for understanding the complexity of SAT, and for experimentally evaluating SAT algorithms. In discussing this we consider the performance of the most popular SAT algorithms on random problems, the theory of average case complexity, the threshold phenomenon, known lower bounds for certain classes of algorithms, and the problem of generating hard instances with solutions.
Local Search Algorithms for SAT: WorstCase Analysis
 In: Proceedings of the 6th Scandinavian Workshop on Algorithm Theory, LNCS 1432
, 1998
"... Recent experiments demonstrated that local search algorithms (e.g. GSAT) are able to find satisfying assignments for many "hard" Boolean formulas. However, no nontrivial worstcase upper bounds were proved, although many such bounds of the form 2 ffn (ff ! 1 is a constant) are known for ..."
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Cited by 3 (3 self)
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Recent experiments demonstrated that local search algorithms (e.g. GSAT) are able to find satisfying assignments for many "hard" Boolean formulas. However, no nontrivial worstcase upper bounds were proved, although many such bounds of the form 2 ffn (ff ! 1 is a constant) are known for other SAT algorithms, e.g. resolutionlike algorithms. In the present paper we prove such a bound for a local search algorithm, namely for CSAT. The class of formulas we consider covers most of DIMACS benchmarks, the satisfiability problem for this class of formulas is NPcomplete. 1 Introduction Recently there has been an increased interest to local search algorithms for the Boolean satisfiability problem. Though this problem is NPcomplete (see e.g. [GaJo]), B. Selman, H. Levesque and D. Mitchell have shown in [SeLeMi] that an algorithm that uses local search can easily handle some of "hard" instances of SAT. They proposed a randomized greedy local search procedure GSAT (see Figure 1) for the Boo...
Criticality and universality in the unitpropagation search rule,” Eur
 Phys. J. B
, 2006
"... Abstract. The probability Psuccess(α, N) that stochastic greedy algorithms successfully solve the random SATisfiability problem is studied as a function of the ratio α of constraints per variable and the number N of variables. These algorithms assign variables according to the unitpropagation (UP) ..."
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Abstract. The probability Psuccess(α, N) that stochastic greedy algorithms successfully solve the random SATisfiability problem is studied as a function of the ratio α of constraints per variable and the number N of variables. These algorithms assign variables according to the unitpropagation (UP) rule in presence of constraints involving a unique variable (1clauses), to some heuristic (H) prescription otherwise. In
Satisfiability threshold of the skewed random kSAT
 In Proceedings, 7th Intl. Conf. on Theory and Applications of Satisfiability Testing
, 2004
"... Abstract. We consider the satisfiability phase transition in skewed random kSAT distributions. It is known that the random kSAT model, in which the instance is a set of m kclauses selected uniformly from the set of all kclauses over n variables, has a satisfiability phase transition at a certain ..."
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Abstract. We consider the satisfiability phase transition in skewed random kSAT distributions. It is known that the random kSAT model, in which the instance is a set of m kclauses selected uniformly from the set of all kclauses over n variables, has a satisfiability phase transition at a certain clause density. The essential feature of the random kSAT is that positive and negative literals occur with equal probability in a random formula. How does the phase transition behavior change as the relative probability of positive and negative literals changes? In this paper we focus on a distribution in which positive and negative literals occur with different probability. We present empirical evidence for the satisfiability phase transition for this distribution. We also prove an upper bound on the satisfiability threshold and a linear lower bound on the number of literals in satisfying partial assignments of skewed random kSAT formulas. 1
Satisfiability for ATPG: Is it easy?
, 1998
"... It has been observed that SAT formulae derived from ATPG problems are efficiently solvable in practise. This seems counterintuitive since SAT is known to be NPComplete. This work seeks to explain this paradox. We identify a certain property of circuits which facilitates efficient solution of ATPG ..."
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It has been observed that SAT formulae derived from ATPG problems are efficiently solvable in practise. This seems counterintuitive since SAT is known to be NPComplete. This work seeks to explain this paradox. We identify a certain property of circuits which facilitates efficient solution of ATPGSAT instances arising from them. In addition, we provide both theoretical proofs and empirical evidence to argue that a large fraction of practical VLSI circuits could be expected to have the said property.
Hard Formulas For SAT Local Search Algorithms
, 1998
"... In 1992 B. Selman, H. Levesque and D. Mitchell proposed GSAT, a greedy local search algorithm for the Boolean satisfiability problem. Good performance of this algorithm and its modifications has been demonstrated by many experimental results. In 1993 I. P. Gent and T. Walsh proposed CSAT, a version ..."
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In 1992 B. Selman, H. Levesque and D. Mitchell proposed GSAT, a greedy local search algorithm for the Boolean satisfiability problem. Good performance of this algorithm and its modifications has been demonstrated by many experimental results. In 1993 I. P. Gent and T. Walsh proposed CSAT, a version of GSAT that almost does not use greediness. It has been recently proved that CSAT can find a satisfying assignment for a restricted class of formulas in the time c n , where c ! 2 is a constant. In this paper we prove a lower bound of the order 2 n for GSAT and CSAT. Namely, we construct formulas F n of n variables, such that GSAT or CSAT finds a satisfying assignment for F n only if this assignment or one of its n neighbours is chosen as the initial assignment for the search. 1 Introduction In the past six years there has been an increased interest to local search algorithms for the Boolean satisfiability problem. Though this problem is NPcomplete (see e.g. [4]), B. Selman, H. Leve...
Random kgdsat Model and its Phase Transition 1
"... Abstract: We present a new type of sat problem called the kgdsat, which generalizes ksat and gdsat. Inkgdsat, clause lengths have geometric distribution, controlled by a probability parameter p; forp =1,akgdsat problem is a ksat problem. We report on the phase transition between satisfiabil ..."
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Abstract: We present a new type of sat problem called the kgdsat, which generalizes ksat and gdsat. Inkgdsat, clause lengths have geometric distribution, controlled by a probability parameter p; forp =1,akgdsat problem is a ksat problem. We report on the phase transition between satisfiability and unsatisfiability for randomly generated instances of kgdsat. We provide theoretical analysis and experimental results suggesting that there is an intriguing relationship (linear in the parameter 1/p) between crossover points for different parameters of kgdsat. Wealso consider a relationship between crossover points for ksat and kgdsat and provide links between these values.