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60
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 ..."
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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...
Solving Problems with Hard and Soft Constraints Using a Stochastic Algorithm for MAXSAT
, 1995
"... Stochastic local search is an effective technique for solving certain classes of large, hard propositional satisfiability problems, including propositional encodings of problems such as circuit synthesis and graph coloring (Selman, Levesque, and Mitchell 1992; Selman, Kautz, and Cohen 1994). Many pr ..."
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Cited by 43 (2 self)
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Stochastic local search is an effective technique for solving certain classes of large, hard propositional satisfiability problems, including propositional encodings of problems such as circuit synthesis and graph coloring (Selman, Levesque, and Mitchell 1992; Selman, Kautz, and Cohen 1994). Many problems of interest to AI and operations research cannot be conveniently encoded as simple satisfiability, because they involve both hard and soft constraints  that is, any solution may have to violate some of the less important constraints. We show how both kinds of constraints can be handled by encoding problems as instances of weighted MAXSAT (finding a model that maximizes the sum of the weights of the satisfied clauses that make up a problem instance). We generalize our localsearch algorithm for satisfiability (GSAT) to handle weighted MAXSAT, and present experimental results on encodings of the Steiner tree problem, which is a wellstudied hard combinatorial search problem. On many...
MaxSolver: An efficient exact algorithm for (weighted) maximum satisfiability
 Artificial Intelligence
, 2005
"... Artificial Intelligence, to appear Maximum Boolean satisfiability (maxSAT) is the optimization counterpart of Boolean satisfiability (SAT), in which a variable assignment is sought to satisfy the maximum number of clauses in a Boolean formula. A branch and bound algorithm based on the DavisPutnam ..."
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Cited by 38 (1 self)
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Artificial Intelligence, to appear Maximum Boolean satisfiability (maxSAT) is the optimization counterpart of Boolean satisfiability (SAT), in which a variable assignment is sought to satisfy the maximum number of clauses in a Boolean formula. A branch and bound algorithm based on the DavisPutnamLogemannLoveland procedure (DPLL) is one of the most competitive exact algorithms for solving maxSAT. In this paper, we propose and investigate a number of strategies for maxSAT. The first strategy is a set of unit propagation or unit resolution rules for maxSAT. We summarize three existing unit propagation rules and propose a new one based on a nonlinear programming formulation of maxSAT. The second strategy is an effective lower bound based on linear programming (LP). We show that the LP lower bound can be made effective as the number of clauses increases. The third strategy consists of a a binaryclause first rule and a dynamicweighting variable ordering rule, which are motivated by a thorough analysis of two existing wellknown variable orderings. Based on the analysis of these strategies, we develop an exact solver for both maxSAT and weighted maxSAT. Our experimental results on random problem instances and many instances from the maxSAT libraries show that our new solver outperforms most of the existing exact maxSAT solvers, with orders of magnitude of improvement in many cases.
SampleSearch: Importance Sampling in Presence of Determinism
, 2009
"... The paper focuses on developing effective importance sampling algorithms for mixed probabilistic and deterministic graphical models. The use of importance sampling in such graphical models is problematic because it generates many useless zero weight samples which are rejected yielding an inefficient ..."
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Cited by 36 (4 self)
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The paper focuses on developing effective importance sampling algorithms for mixed probabilistic and deterministic graphical models. The use of importance sampling in such graphical models is problematic because it generates many useless zero weight samples which are rejected yielding an inefficient sampling process. To address this rejection problem, we propose the SampleSearch scheme that augments sampling with systematic constraintbased backtracking search. We characterize the bias introduced by the combination of search with sampling, and derive a weighting scheme which yields an unbiased estimate of the desired statistics (e.g. probability of evidence). When computing the weights exactly is too complex, we propose an approximation which has a weaker guarantee of asymptotic unbiasedness. We present results of an extensive empirical evaluation demonstrating that SampleSearch outperforms other schemes in presence of significant amount of determinism.
A General Scheme for Automatic Generation of Search Heuristics from Specification Dependencies
 Artificial Intelligence
, 2001
"... The paper presents and evaluates the power of a new scheme that generates search heuristics mechanically for problems expressed using a set of functions or relations over a finite set of variables. The heuristics are extracted from a parameterized approximation scheme called MiniBucket eliminati ..."
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Cited by 34 (17 self)
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The paper presents and evaluates the power of a new scheme that generates search heuristics mechanically for problems expressed using a set of functions or relations over a finite set of variables. The heuristics are extracted from a parameterized approximation scheme called MiniBucket elimination that allows controlled tradeoff between computation and accuracy. The heuristics are used to guide BranchandBound and BestFirst search. Their performance is compared on two optimization tasks: the MaxCSP task defined on deterministic databases and the Most Probable Explanation task defined on probabilistic databases. Benchmarks were random data sets as well as applications to coding and medical diagnosis problems. Our results demonstrate that the heuristics generated are effective for both search schemes, permitting controlled tradeoff between preprocessing (for heuristic generation) and search.
Exploiting Variable Dependency in Local Search
 In Abstracts of the Poster Sessions of IJCAI97
, 1997
"... Stochastic search has recently been shown to be successful for solving large boolean satisfiability problems. However, systematic methods tend to be more effective in problem domains with a large number of dependent variables: that is, variables whose truth values are directly determined by a smalle ..."
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Cited by 23 (1 self)
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Stochastic search has recently been shown to be successful for solving large boolean satisfiability problems. However, systematic methods tend to be more effective in problem domains with a large number of dependent variables: that is, variables whose truth values are directly determined by a smaller set of independent variables. In systematic search, truth values can be efficiently propagated from the independent to the dependent variables by unit propagation. Such propagation is more expensive in traditional stochastic procedures. In this paper we propose a mechanism for effectively dealing with dependent variables in stochastic search. We also provide empirical data showing the procedure outperforms the best previous stochastic and systematic search procedures on large formulas with a high ratio of dependent to independent variables. 1 Introduction Recent years have seen significant progress in our ability to solve large propositional satisfiability problems. Randomly generated pro...
Using WalkSAT and RelSAT for cryptographic key search
 In Proceedings of the International Joint Conference on Arti Intelligence
, 1999
"... Computer security depends heavily on the strength of cryptographic algorithms. Thus, cryptographic key search is often THE search problem for many governments and corporations. In the recent years, Al search techniques have achieved notable successes in solving "real world" problem ..."
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Cited by 21 (0 self)
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Computer security depends heavily on the strength of cryptographic algorithms. Thus, cryptographic key search is often THE search problem for many governments and corporations. In the recent years, Al search techniques have achieved notable successes in solving &quot;real world&quot; problems. Following a recent result which showed that the properties of the U.S. Data Encryption Standard can be encoded in propositional logic, this paper advocates the use of cryptographic key search as a benchmark for propositional reasoning and search. Benchmarks based on the encoding of cryptographic algorithms optimally share the features of &quot;real world &quot; and random problems. In this paper, two stateoftheart Al search algorithms, WalkSAT by Kautz & Selman and RelSAT by Bayardo & Schrag, have been tested on the encoding of the Data Encryption Standard, to see whether they are up the task, and we discuss what lesson can be learned from the analysis on this benchmark to improve SAT solvers. New challenges in this field conclude the paper. 1
SymmetryBreaking for PseudoBoolean Formulas
, 2003
"... Many important tasks in circuit design and verification can be performed in practice via reductions to Boolean Satisfiability (SAT), making SAT a fundamental EDA problem. However such reductions often leave out applicationspecific structure, thus handicapping EDA tools in their competition with cre ..."
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Cited by 17 (11 self)
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Many important tasks in circuit design and verification can be performed in practice via reductions to Boolean Satisfiability (SAT), making SAT a fundamental EDA problem. However such reductions often leave out applicationspecific structure, thus handicapping EDA tools in their competition with creative engineers. Successful attempts to represent and utilize additional structure on Boolean variables include recent work on 01 Integer Linear Programming (ILP) and on symmetries in SAT. Those extensions gracefully...
THE SAT PROBLEM OF SIGNED CNF FORMULAS
"... Signed conjunctive normal form (signed CNF) is a classical conjunctive clause form using a generalised notion of literal, called signed literal. A signed literal is an expression of the form S: p, where p is a classical atom and S, its sign, is a subset of a domain N. The informal meaning is “p ta ..."
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Cited by 15 (10 self)
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Signed conjunctive normal form (signed CNF) is a classical conjunctive clause form using a generalised notion of literal, called signed literal. A signed literal is an expression of the form S: p, where p is a classical atom and S, its sign, is a subset of a domain N. The informal meaning is “p takes one of the values in S”. Signed formulas are a logical language for knowledge representation that lies in the intersection of the areas constraint programming (CP), manyvalued logic (MVL), and annotated logic programming (ALP). This central rôle of signed CNF justifies a detailed study of its subclasses including algorithms for and complexities of associated satisfiability problems (SAT problems). Although signed logic is used since the 1960s, there are only few systematic investigations of its properties. In contrast to work done in ALP and MVL, our present work is a more finegrained study for the case of propositional CNF. We highlight the most interesting lines of current research: (i) signed versions of some main proponents of 1 2 LABELLED DEDUCTION classical deduction systems including nontrivial refinements having no classical counterpart; (ii) incomplete local search methods for satisfiability checking of signed formulas; (iii) phase transition phenomena as known, for example, from classical SAT and the influence of the cardinality of N on the crossover point; (iv) the complexity of the SAT problem for signed CNF and its subclasses.