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36
Using CSP lookback techniques to solve realworld SAT instances
, 1997
"... We report on the performance of an enhanced version of the “DavisPutnam ” (DP) proof procedure for propositional satisfiability (SAT) on large instances derived from realworld problems in planning, scheduling, and circuit diagnosis and synthesis. Our results show that incorporating CSP lookback tec ..."
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Cited by 238 (1 self)
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We report on the performance of an enhanced version of the “DavisPutnam ” (DP) proof procedure for propositional satisfiability (SAT) on large instances derived from realworld problems in planning, scheduling, and circuit diagnosis and synthesis. Our results show that incorporating CSP lookback techniques especially the relatively new technique of relevancebounded learning renders easy many problems which otherwise are beyond DP’s reach. Frequently they make DP, a systematic algorithm, perform as well or better than stochastic SAT algorithms such as GSAT or WSAT. We recommend that such techniques be included as options in implementations of DP, just as they are in systematic algorithms for the more general constraint satisfaction problem.
Depthbounded Discrepancy Search
 In Proceedings of IJCAI97
, 1997
"... Many search trees are impractically large to explore exhaustively. Recently, techniques like limited discrepancy search have been proposed for improving the chance of finding a goal in a limited amount of search. Depthbounded discrepancy search offers such a hope. The motivation behind depthbounde ..."
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Cited by 87 (0 self)
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Many search trees are impractically large to explore exhaustively. Recently, techniques like limited discrepancy search have been proposed for improving the chance of finding a goal in a limited amount of search. Depthbounded discrepancy search offers such a hope. The motivation behind depthbounded discrepancy search is that branching heuristics are more likely to be wrong at the top of the tree than at the bottom. We therefore combine one of the best features of limited discrepancy search  the ability to undo early mistakes  with the completeness of iterative deepening search. We show theoretically and experimentally that this novel combination outperforms existing techniques. 1 Introduction On backtracking, depthfirst search explores decisions made against the branching heuristic (or "discrepancies "), starting with decisions made deep in the search tree. However, branching heuristics are more likely to be wrong at the top of the tree than at the bottom. We would like theref...
Using CSP LookBack Techniques to Solve RealWorld SAT Instances
, 1997
"... We report on the performance of an enhanced version of the "DavisPutnam" (DP) proof procedure for propositional satisfiability (SAT) on large instances derived from realworld problems in planning, scheduling, and circuit diagnosis and synthesis. Our results show that incorporating CSP ..."
Abstract

Cited by 46 (0 self)
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We report on the performance of an enhanced version of the "DavisPutnam" (DP) proof procedure for propositional satisfiability (SAT) on large instances derived from realworld problems in planning, scheduling, and circuit diagnosis and synthesis. Our results show that incorporating CSP lookback techniques  especially the relatively new technique of relevancebounded learning  renders easy many problems which otherwise are beyond DP's reach. Frequently they make DP, a systematic algorithm, perform as well or better than stochastic SAT algorithms such as GSAT or WSAT. We recommend that such techniques be included as options in implementations of DP, just as they are in systematic algorithms for the more general constraint satisfaction problem. Introduction While CNF propositional satisfiability (SAT) is a specific kind constraint satisfaction problem (CSP), until recently there has been little application of popular CSP lookback techniques in SAT algorithms. In previo...
Backbone Fragility and the Local Search Cost Peak
 Journal of Artificial Intelligence Research
, 2000
"... The local search algorithm WSat is one of the most successful algorithms for solving the satisfiability (SAT) problem. It is notably e#ective at solving hard Random 3SAT instances near the socalled `satisfiability threshold', but still shows a peak in search cost near the threshold and lar ..."
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Cited by 45 (3 self)
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The local search algorithm WSat is one of the most successful algorithms for solving the satisfiability (SAT) problem. It is notably e#ective at solving hard Random 3SAT instances near the socalled `satisfiability threshold', but still shows a peak in search cost near the threshold and large variations in cost over di#erent instances. We make a number of significant contributions to the analysis of WSat on highcost random instances, using the recentlyintroduced concept of the backbone of a SAT instance. The backbone is the set of literals which are entailed by an instance. We find that the number of solutions predicts the cost well for smallbackbone instances but is much less relevant for the largebackbone instances which appear near the threshold and dominate in the overconstrained region. We show a very strong correlation between search cost and the Hamming distance to the nearest solution early in WSat's search. This pattern leads us to introduce a measure of the ba...
Balance and Filtering in Structured Satisfiable Problems
 In IJCAI
, 2001
"... New methods to generate hard random problem instances have driven progress on algorithms for deduction and constraint satisfaction. Recently Achlioptas et al. (AAAI 2000) introduced a new generator based on Latin squares that creates only satisfiable problems, and so can be used to accurately test i ..."
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Cited by 43 (13 self)
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New methods to generate hard random problem instances have driven progress on algorithms for deduction and constraint satisfaction. Recently Achlioptas et al. (AAAI 2000) introduced a new generator based on Latin squares that creates only satisfiable problems, and so can be used to accurately test incomplete (one sided) solvers. We investigate how this and other generators are biased away from the uniform distribution of satisfiable problems and show how they can be improved by imposing a balance condition. More generally, we show that the generator is one member of a family of related models that generate distributions ranging from ones that are everywhere tractable to ones that exhibit a sharp hardness threshold. We also discuss the critical role of the problem encoding in the performance of both systematic and local search solvers.
The complexity of propositional proofs
 Bulletin of Symbolic Logic
"... Abstract. Propositional proof complexity is the study of the sizes of propositional proofs, and more generally, the resources necessary to certify propositional tautologies. Questions about proof sizes have connections with computational complexity, theories of arithmetic, and satisfiability algorit ..."
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Cited by 31 (0 self)
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Abstract. Propositional proof complexity is the study of the sizes of propositional proofs, and more generally, the resources necessary to certify propositional tautologies. Questions about proof sizes have connections with computational complexity, theories of arithmetic, and satisfiability algorithms. This is article includes a broad survey of the field, and a technical exposition of some recently developed techniques for proving lower bounds on proof sizes. Contents
Extending forward checking
 in Proceedings of CP’00
, 2000
"... Abstract. Among backtracking based algorithms for constraint satisfaction problems (CSPs), algorithms employing constraint propagation, like forward checking (FC) and MAC, have had the most practical impact. These algorithms use constraint propagation during search to prune inconsistent values from ..."
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Cited by 19 (4 self)
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Abstract. Among backtracking based algorithms for constraint satisfaction problems (CSPs), algorithms employing constraint propagation, like forward checking (FC) and MAC, have had the most practical impact. These algorithms use constraint propagation during search to prune inconsistent values from the domains of the uninstantiated variables. In this paper we present a general approach to extending constraint propagating algorithms, especially forward checking. In particular, we provide a simple yet flexible mechanism for pruning domain values, and show that with this in place it becomes easy to utilize new mechanisms for detecting inconsistent values during search. This leads to a powerful and uniform technique for designing new CSP algorithms: one simply need design new methods for detecting inconsistent values and then interface them with the domain pruning mechanism. Furthermore, we also show that algorithms following this design can proved to be correct in a simple and uniform way. To demonstrate the utility of these ideas five “new ” CSP algorithms are presented. 1
A New Look at the EasyHardEasy Pattern of Combinatorial Search Difficulty
 Journal of Artificial Intelligence Research
, 1997
"... The easyhardeasy pattern in the difficulty of combinatorial search problems as constraints are added has been explained as due to a competition between the decrease in number of solutions and increased pruning. We test the generality of this explanation by examining one of its predictions: if the ..."
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Cited by 17 (2 self)
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The easyhardeasy pattern in the difficulty of combinatorial search problems as constraints are added has been explained as due to a competition between the decrease in number of solutions and increased pruning. We test the generality of this explanation by examining one of its predictions: if the number of solutions is held fixed by the choice of problems, then increased pruning should lead to a monotonic decrease in search cost. Instead, we find the easyhardeasy pattern in median search cost even when the number of solutions is held constant, for some search methods. This generalizes previous observations of this pattern and shows that the existing theory does not explain the full range of the peak in search cost. In these cases the pattern appears to be due to changes in the size of the minimal unsolvable subproblems, rather than changing numbers of solutions. 1. Introduction Recently, many authors have shown that the solution cost for various kinds of combinatorial search probl...
The search for Satisfaction
, 1999
"... In recent years, there has been an explosion of research in AI into propositional satis ability (or Sat). There are many factors behind the increased interest in this area. One factor is the improvement in search procedures for Sat. New local search procedures like Gsat are able to solve Sat problem ..."
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Cited by 14 (1 self)
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In recent years, there has been an explosion of research in AI into propositional satis ability (or Sat). There are many factors behind the increased interest in this area. One factor is the improvement in search procedures for Sat. New local search procedures like Gsat are able to solve Sat problems with thousands of variables. At the same time, implementations of complete search algorithms like DavisPutnam have been able to solve open mathematical problems. Another factor is the identi cation of hard Sat problems at a phase transition in solubility. A third factor is the demonstration that we can often solve real world problems by encoding them into Sat. There has also seen an improved theoretical understanding of Sat, particularly in the analysis of such phase transition behaviour. This paper reviews the state of the art for research into satis ability, and discuss applications in which algorithms for satis ability have proved successful.
Regular random ksat: Properties of balanced formulas
 Journal of Automated Reasoning
, 2005
"... Abstract. We consider a model for generating random kSAT formulas, in which each literal occurs approximately the same number of times in the formula clauses (regular random kSAT). Our experimental results show that such regular random kSAT instances are much harder than the usual uniform random ..."
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Cited by 13 (2 self)
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Abstract. We consider a model for generating random kSAT formulas, in which each literal occurs approximately the same number of times in the formula clauses (regular random kSAT). Our experimental results show that such regular random kSAT instances are much harder than the usual uniform random kSAT problems. This is in agreement with other results that show that more balanced instances of random combinatorial problems are often much more difficult to solve than uniformly random instances, even at phase transition boundaries. There are almost no formal results known for such problem distributions. The balancing constraints add a dependency between variables that complicates a standard analysis. Regular random 3SAT exhibits a phase transition as a function of the ratio α of clauses to variables. The transition takes place at approximately α =3.5. We will show that for α>3.78 w.h.p. 1 random Regular 3SAT formulas are unsatisfiable. We will also show that the analysis of a greedy algorithm proposed in Kaporis et al (KKL02) for the uniform 3SAT model can be adapted for regular random 3SAT. In particular, we show that for formulas with ratio α<2.46, a greedy algorithm finds a satisfying assignment with positive probability. 1.