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155
Bounded model checking
, 2009
"... Besides Equivalence Checking [KK97, KPKG02] the most important industrial application of SAT is currently Bounded Model Checking (BMC) [BCCZ99]. Both techniques are used for formal hardware verification in the context of electronic design automation (EDA), but have successfully been applied to many ..."
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Cited by 165 (3 self)
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Besides Equivalence Checking [KK97, KPKG02] the most important industrial application of SAT is currently Bounded Model Checking (BMC) [BCCZ99]. Both techniques are used for formal hardware verification in the context of electronic design automation (EDA), but have successfully been applied to many other domains as well. In this chapter, we focus on BMC. In practice, BMC is mainly used for falsification resp. testing, which is concerned with violations of temporal properties. However, the original paper on BMC [BCCZ99] already discussed extensions that can prove properties. A considerable part of this chapter discusses these complete extensions, which are often called “unbounded ” model checking techniques, even though they are build upon the same principles as plain BMC. Two further related applications, in which BMC becomes more and more important, are automatic test case generation for closing coverage holes, and disproving redundancy in designs. Most of the techniques discussed in this chapter transfer to this more general setting as well, even though our focus is on property
Constructing Conditional Plans by a TheoremProver
 Journal of Artificial Intelligence Research
, 1999
"... The research on conditional planning rejects the assumptions that there is no uncertainty or incompleteness of knowledge with respect to the state and changes of the system the plans operate on. Without these assumptions the sequences of operations that achieve the goals depend on the initial sta ..."
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Cited by 155 (6 self)
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The research on conditional planning rejects the assumptions that there is no uncertainty or incompleteness of knowledge with respect to the state and changes of the system the plans operate on. Without these assumptions the sequences of operations that achieve the goals depend on the initial state and the outcomes of nondeterministic changes in the system. This setting raises the questions of how to represent the plans and how to perform plan search. The answers are quite different from those in the simpler classical framework. In this paper, we approach conditional planning from a new viewpoint that is motivated by the use of satisfiability algorithms in classical planning. Translating conditional planning to formulae in the propositional logic is not feasible because of inherent computational limitations. Instead, we translate conditional planning to quantified Boolean formulae. We discuss three formalizations of conditional planning as quantified Boolean formulae, and pr...
Resolve and Expand
 IN PROC. OF SAT’04
, 2004
"... We present a novel expansion based decision procedure for quantified boolean formulas (QBF) in conjunctive normal form (CNF). The basic idea is to resolve existentially quantified variables and eliminate universal variables by expansion. This process is continued until the formula becomes propositi ..."
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Cited by 134 (18 self)
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We present a novel expansion based decision procedure for quantified boolean formulas (QBF) in conjunctive normal form (CNF). The basic idea is to resolve existentially quantified variables and eliminate universal variables by expansion. This process is continued until the formula becomes propositional and can be solved by any SAT solver. On structured problems our implementation quantor is competitive with stateoftheart QBF solvers based on DPLL. It is orders of magnitude faster on certain hard to solve instances.
Backjumping for Quantified Boolean Logic Satisfiability
 ARTIFICIAL INTELLIGENCE
, 2001
"... The implementation of effective reasoning tools for deciding the satisfiability of Quantified Boolean Formulas (QBFs) is an important research issue in Artificial Intelligence. Many decision procedures have been proposed in the last few years, most of them based on the Davis, Logemann, Loveland ..."
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Cited by 80 (6 self)
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The implementation of effective reasoning tools for deciding the satisfiability of Quantified Boolean Formulas (QBFs) is an important research issue in Artificial Intelligence. Many decision procedures have been proposed in the last few years, most of them based on the Davis, Logemann, Loveland procedure (DLL) for propositional satisfiability (SAT). In this paper we show how it is possible to extend the conflictdirected backjumping schema for SAT to QBF: when applicable, it allows to jump over existentially quantified literals while backtracking. We introduce solutiondirected backjumping, which allows the same for universally quantified literals. Then, we show how it is possible to incorporate both conflictdirected and solutiondirected backjumping in a DLLbased decision procedure for QBF satisfiability. We also implement and test the procedure: The experimental analysis shows that, because of backjumping, significant speedups can be obtained. While there have been several proposals for backjumping in SAT, this is the first time as far as we know this idea has been proposed, implemented and experimented for QBFs.
QUBE: A system for deciding quantified boolean formulas satisfiability
, 2001
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Improvements to the evaluation of quantified Boolean formulae
 In Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence (IJCAI'99), July 31August 6
, 1999
"... We present a theoremprover for quantified Boolean formulae and evaluate it on random quantified formulae and formulae that represent problems from automated planning. Even though the notion of quantified Boolean formula is theoretically important, automated reasoning with QBF has not been thoroughl ..."
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Cited by 76 (3 self)
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We present a theoremprover for quantified Boolean formulae and evaluate it on random quantified formulae and formulae that represent problems from automated planning. Even though the notion of quantified Boolean formula is theoretically important, automated reasoning with QBF has not been thoroughly investigated. Universal quantifiers are needed in representing many computational problems that cannot be easily translated to the propositional logic and solved by satisfiability algorithms. Therefore efficient reasoning with QBF is important. The DavisPutnam procedure can be extended to evaluate quantified Boolean formulae. A straightforward algorithm of this kind is not very efficient. We identify universal quantifiers as the main area where improvements to the basic algorithm can be made. We present a number of techniques for reducing the amount of search that is needed, and evaluate their effectiveness by running the algorithm on a collection of formulae obtained from planning and generated randomly. For the structured problems we consider, the techniques lead to a dramatic speedup. 1
Solving Advanced Reasoning Tasks using Quantified Boolean Formulas
, 2000
"... We consider the compilation of different reasoning tasks into the evaluation problem of quantified boolean formulas (QBFs) as an approach to develop prototype reasoning systems useful, e.g., for experimental purposes. ..."
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Cited by 72 (20 self)
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We consider the compilation of different reasoning tasks into the evaluation problem of quantified boolean formulas (QBFs) as an approach to develop prototype reasoning systems useful, e.g., for experimental purposes.
Conflict Driven Learning in a Quantified Boolean Satisfiability Solver
 in Proc. of ICCAD
, 2002
"... Within the verification community, there has been a recent increase in interest in Quantified Boolean Formula evaluation (QBF) as many interesting sequential circuit verification problems can be formulated as QBF instances. A closely related research area to QBF is Boolean Satisfiability (SAT). Rece ..."
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Cited by 70 (3 self)
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Within the verification community, there has been a recent increase in interest in Quantified Boolean Formula evaluation (QBF) as many interesting sequential circuit verification problems can be formulated as QBF instances. A closely related research area to QBF is Boolean Satisfiability (SAT). Recent advances in SAT research have resulted in some very efficient SAT solvers. One of the critical techniques employed in these solvers is Conflict Driven Learning. In this paper, we adapt conflict driven learning for application in a QBF setting. We show that conflict driven learning can be regarded as a resolution process on the clauses. We prove that under certain conditions, tautology clauses obtained from resolution in QBF also obey the rules for implication and conflicts of regular (nontautology) clauses; and therefore they can be treated as regular clauses and used in future search. We have implemented this idea in a new QBF solver called Quaffle and our initial experiments show that conflict driven learning can greatly speed up the solution process for most of the benchmarks we tested. 1.
Stochastic Boolean Satisfiability
 Journal of Automated Reasoning
, 2000
"... . Satisfiability problems and probabilistic models are core topics of artificial intelligence and computer science. This paper looks at the rich intersection between these two areas, opening the door for the use of satisfiability approaches in probabilistic domains. The paper examines a generic stoc ..."
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Cited by 63 (9 self)
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. Satisfiability problems and probabilistic models are core topics of artificial intelligence and computer science. This paper looks at the rich intersection between these two areas, opening the door for the use of satisfiability approaches in probabilistic domains. The paper examines a generic stochastic satisfiability problem, SSat, which can function for probabilistic domains as Sat does for deterministic domains. It shows the connection between SSat and well studied problems in belief network inference and planning under uncertainty, and defines algorithms, both systematic and stochastic, for solving SSat instances. These algorithms are validated on random SSat formulae generated under the fixedclause model. In spite of the large complexity gap between SSat (PSPACE) and Sat (NP), the paper suggests that much of what we've learned about Sat transfers to the probabilistic domain. 1. Introduction There has been a recent focus in artificial intelligence (AI) on solving problems exh...
Lemma and model caching in decision procedures for quantified boolean formulas
 In TABLEAUX 2002
, 2002
"... Abstract. The increasingrole of quantified Boolean logic in many applications calls for practically efficient decision procedures. One of the most promisingparadigms is the semantic tree format implemented in the style of the DPLL procedure. In this paper, socalled learningtechniques like intellige ..."
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Cited by 62 (0 self)
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Abstract. The increasingrole of quantified Boolean logic in many applications calls for practically efficient decision procedures. One of the most promisingparadigms is the semantic tree format implemented in the style of the DPLL procedure. In this paper, socalled learningtechniques like intelligent backtrackingand cachingof lemmas which proved useful in the pure propositional case are generalised to the quantified Boolean case and the occuringdifferences are discussed. Due to the strongrestriction of the variable selection in semantic tree procedures for quantified Boolean formulas, learningmethods are more important than in the propositional case, as we demonstrate. Furthermore, in addition to the cachingof lemmas, significant advances can be achieved by techniques based on the caching of models, too. The theoretical effect of these improvements is illustrated by a comparison of the search spaces on pathological examples. We also describe the basic features of the system Semprop, which is an efficient implementation of (some of) the developed techniques, and give the results of an experimental evaluation of the system on a number of practical examples. 1