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The Quest for Efficient Boolean Satisfiability Solvers
, 2002
"... has seen much interest in not just the theoretical computer science community, but also in areas where practical solutions to this problem enable significant practical applications. Since the first development of the basic search based algorithm proposed by Davis, Putnam, Logemann and Loveland (DPLL ..."
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Cited by 144 (3 self)
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has seen much interest in not just the theoretical computer science community, but also in areas where practical solutions to this problem enable significant practical applications. Since the first development of the basic search based algorithm proposed by Davis, Putnam, Logemann and Loveland (DPLL) about forty years ago, this area has seen active research effort with many interesting contributions that have culminated in stateoftheart SAT solvers today being able to handle problem instances with thousands, and in same cases even millions, of variables. In this paper we examine some of the main ideas along this passage that have led to our current capabilities. Given the depth of the literature in this field, it is impossible to do this in any comprehensive way; rather we focus on techniques with consistent demonstrated efficiency in available solvers. For the most part, we focus on techniques within the basic DPLL search framework, but also briefly describe other approaches and look at some possible future research directions. 1.
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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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.
Towards a symmetric treatment of satisfaction and conflicts in quantified boolean formula evaluation
, 2002
"... In this paper, we describe a new framework for evaluating Quantified Boolean Formulas (QBF). The new framework is based on the DavisPutnam (DPLL) search algorithm. In existing DPLL based QBF algorithms, the problem database is represented in Conjunctive Normal Form (CNF) as a set of clauses, impli ..."
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Cited by 56 (3 self)
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In this paper, we describe a new framework for evaluating Quantified Boolean Formulas (QBF). The new framework is based on the DavisPutnam (DPLL) search algorithm. In existing DPLL based QBF algorithms, the problem database is represented in Conjunctive Normal Form (CNF) as a set of clauses, implications are generated from these clauses, and backtracking in the search tree is chronological. In this work, we augment the basic DPLL algorithm with conflict driven learning as well as satisfiability directed implication and learning. In addition to the traditional clause database, we add a cube database to the data structure. We show that cubes can be used to generate satisfiability directed implications similar to conflict directed implications generated by the clauses. We show that in a QBF setting, conflicting leaves and satisfying leaves of the search tree both provide valuable information to the solver in a symmetric way. We have implemented our algorithm in the new QBF solver Quaffle. Experimental results show that for some test cases, satisfiability directed implication and learning significantly prunes the search.
SEARCHING FOR TRUTH: TECHNIQUES FOR SATISFIABILITY OF BOOLEAN FORMULAS
, 2003
"... I certify that I have read this thesis and that in my opinion it is fully adequate, in scope and in quality, as a dissertation for the degree of Doctor of Philosophy. ..."
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I certify that I have read this thesis and that in my opinion it is fully adequate, in scope and in quality, as a dissertation for the degree of Doctor of Philosophy.
On subsumption removal and onthefly cnf simplification
 in: Proceedings of the International Conference on Theory and Applications of Satisfiability Testing (SAT’05), 2005
"... Abstract. Conjunctive Normal Form (CNF) Boolean formulas generated from resolution or solution enumeration often have much redundancy. It is desirable to have an efficient algorithm to simplify and compact such CNF formulas on the fly. Given a clause in a CNF formula, if a subset of its literals con ..."
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Abstract. Conjunctive Normal Form (CNF) Boolean formulas generated from resolution or solution enumeration often have much redundancy. It is desirable to have an efficient algorithm to simplify and compact such CNF formulas on the fly. Given a clause in a CNF formula, if a subset of its literals constitutes another clause in the formula, then the first clause is said to be subsumed by the second clause. A subsumed clause is redundant and can be removed from the original formula. In this paper, we present a novel algorithm to maintain a subsumptionfree CNF clause database by efficiently detecting and removing subsumption as the clauses are being added. Furthermore, we present an algorithm that compact the database greedily by recursively applying resolutions that decrement the size of the clause database. Our experimental evaluations show that these algorithms are efficient and effective in practice. 1