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25
Hard and Easy Distributions of SAT Problems
, 1992
"... We report results from largescale experiments in satisfiability testing. As has been observed by others, testing the satisfiability of random formulas often appears surprisingly easy. Here we show that by using the right distribution of instances, and appropriate parameter values, it is possible to ..."
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Cited by 219 (17 self)
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We report results from largescale experiments in satisfiability testing. As has been observed by others, testing the satisfiability of random formulas often appears surprisingly easy. Here we show that by using the right distribution of instances, and appropriate parameter values, it is possible to generate random formulas that are hard, that is, for which satisfiability testing is quite difficult. Our results provide a benchmark for the evaluation of satisfiabilitytesting procedures. Introduction Many computational tasks of interest to AI, to the extent that they can be precisely characterized at all, can be shown to be NPhard in their most general form. However, there is fundamental disagreement, at least within the AI community, about the implications of this. It is claimed on the one hand that since the performance of algorithms designed to solve NPhard tasks degrades rapidly with small increases in input size, something will need to be given up to obtain acceptable behavior....
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...
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 114 (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.
The Complexity Of Propositional Proofs
 Bulletin of Symbolic Logic
, 1995
"... This paper of Tseitin is a landmark as the first to give nontrivial lower bounds for propositional proofs; although it predates the first papers on ..."
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Cited by 105 (2 self)
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This paper of Tseitin is a landmark as the first to give nontrivial lower bounds for propositional proofs; although it predates the first papers on
Generating Hard Satisfiability Problems
 Artificial Intelligence
, 1996
"... We report results from largescale experiments in satisfiability testing. As has been observed by others, testing the satisfiability of random formulas often appears surprisingly easy. Here we show that by using the right distribution of instances, and appropriate parameter values, it is possible ..."
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Cited by 98 (2 self)
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We report results from largescale experiments in satisfiability testing. As has been observed by others, testing the satisfiability of random formulas often appears surprisingly easy. Here we show that by using the right distribution of instances, and appropriate parameter values, it is possible to generate random formulas that are hard, that is, for which satisfiability testing is quite difficult. Our results provide a benchmark for the evaluation of satisfiabilitytesting procedures. In Artificial Intelligence, 81 (19996) 1729. 1 Introduction Many computational tasks of interest to AI, to the extent that they can be precisely characterized at all, can be shown to be NPhard in their most general form. However, there is fundamental disagreement, at least within the AI community, about the implications of this. It is claimed on the one hand that since the performance of algorithms designed to solve NPhard tasks degrades rapidly with small increases in input size, something ...
Resolution versus Search: Two Strategies for SAT
 Journal of Automated Reasoning
, 2000
"... The paper compares two popular strategies for solving propositional satisfiability, backtracking search and resolution, and analyzes the complexity of a directional resolution algorithm (DR) as a function of the "width" (w) of the problem's graph. ..."
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Cited by 51 (1 self)
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The paper compares two popular strategies for solving propositional satisfiability, backtracking search and resolution, and analyzes the complexity of a directional resolution algorithm (DR) as a function of the "width" (w) of the problem's graph.
The History and Status of the P versus NP Question
, 1992
"... this article, I have attempted to organize and describe this literature, including an occasional opinion about the most fruitful directions, but no technical details. In the first half of this century, work on the power of formal systems led to the formalization of the notion of algorithm and the re ..."
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Cited by 50 (0 self)
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this article, I have attempted to organize and describe this literature, including an occasional opinion about the most fruitful directions, but no technical details. In the first half of this century, work on the power of formal systems led to the formalization of the notion of algorithm and the realization that certain problems are algorithmically unsolvable. At around this time, forerunners of the programmable computing machine were beginning to appear. As mathematicians contemplated the practical capabilities and limitations of such devices, computational complexity theory emerged from the theory of algorithmic unsolvability. Early on, a particular type of computational task became evident, where one is seeking an object which lies
Deciding propositional tautologies: Algorithms and their complexity
, 1997
"... We investigate polynomial reductions and efficient branching rules for algorithms deciding propositional tautologies for DNF and coNPcomplete subclasses. Upper bounds on the time complexity are given with exponential part 2 ff\Delta(F ) where (F ) is one of the measures n(F ) = #f variables g, ` ..."
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Cited by 38 (8 self)
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We investigate polynomial reductions and efficient branching rules for algorithms deciding propositional tautologies for DNF and coNPcomplete subclasses. Upper bounds on the time complexity are given with exponential part 2 ff\Delta(F ) where (F ) is one of the measures n(F ) = #f variables g, `(F ) = #f literal occurrences g and k(F ) = #f clauses g. We start with a discussion of variants of the algorithms from [Monien/Speckenmeyer85] and [Luckhardt84] with the known upper bound 2 0:695\Deltan for 3DNF and (roughly) (2 \Delta (1 \Gamma 2 \Gammap )) n for pDNF, p 3, where p is the maximal clause length, giving now an uniform treatment for all pDNF including the easy decidable case p 2. Recently for 3DNF the bound has been lowered to 2 0:5892\Deltan ([K2]; see also [Sch2], [K3]). In this article further improvements are achieved by studying two additional characteristic groups of parameters. The first group differentiates according to the maximal numbers (a; b) of occ...
MultiResolution on Compressed Sets of Clauses
 Proc. of 12th International Conference on Tools with Artificial Intelligence (ICTAI2000
, 2000
"... This paper presents a system based on new operators for handling sets of propositional clauses represented by means of ZBDDs. The high compression power of such data structures allows efficient encodings of structured instances. A specialized operator for the distribution of sets of clauses is intro ..."
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Cited by 31 (4 self)
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This paper presents a system based on new operators for handling sets of propositional clauses represented by means of ZBDDs. The high compression power of such data structures allows efficient encodings of structured instances. A specialized operator for the distribution of sets of clauses is introduced and used for performing multiresolution on clause sets. Cut eliminations between sets of clauses of exponential size may then be performed using polynomial size data structures. The ZRES system, a new implementation of the DavisPutnam procedure of 1960, solves two hard problems for resolution, that are currently out of the scope of the best SAT provers. 1
Global Optimization for Satisfiability (SAT) Problem
, 1994
"... The satisfiability (SAT) problem is a fundamental problem in mathematical logic, inference, automated reasoning, VLSI engineering, and computing theory. In this paper, following CNF and DNF local search methods, we introduce the Universal SAT problem model, UniSAT, that transforms the discrete SAT ..."
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Cited by 20 (3 self)
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The satisfiability (SAT) problem is a fundamental problem in mathematical logic, inference, automated reasoning, VLSI engineering, and computing theory. In this paper, following CNF and DNF local search methods, we introduce the Universal SAT problem model, UniSAT, that transforms the discrete SAT problem on Boolean space f0; 1g m into an unconstrained global optimization problem on real space E m . A direct correspondence between the solution of the SAT problem and the global minimum point of the UniSAT objective function is established. Many existing global optimization algorithms can be used to solve the UniSAT problems. Combined with backtracking /resolution procedures, a global optimization algorithm is able to verify satisfiability as well as unsatisfiability. This approach achieves significant performance improvements for certain classes of conjunctive normal form (CNF ) formulas. It offers a complementary approach to the existing SAT algorithms.