Results 1  10
of
64
An Algorithm to Evaluate Quantified Boolean Formulae and its Experimental Evaluation
 Journal of Automated Reasoning
, 1999
"... The high computational complexity of advanced reasoning tasks such as reasoning about knowledge and planning calls for efficient and reliable algorithms for reasoning problems harder than NP. In this paper we propose Evaluate, an algorithm for evaluating Quantified Boolean Formulae, a language that ..."
Abstract

Cited by 141 (2 self)
 Add to MetaCart
The high computational complexity of advanced reasoning tasks such as reasoning about knowledge and planning calls for efficient and reliable algorithms for reasoning problems harder than NP. In this paper we propose Evaluate, an algorithm for evaluating Quantified Boolean Formulae, a language that extends propositional logic in a way such that many advanced forms of propositional reasoning, e.g., circumscription, can be easily formulated as evaluation of a QBF. Algorithms for evaluation of QBFs are suitable for the experimental analysis on a wide range of complexity classes, a property not easily found in other formalisms. Evaluate is based on a generalization of the DavisPutnam procedure for SAT, and is guaranteed to work in polynomial space. Before presenting the algorithm, we discuss several abstract properties of QBFs that we singled out to make it more efficient. We also discuss various options that were investigated about heuristics and data structures, and report the main res...
Resolve and Expand
 In Proc. of SAT’04
, 2004
"... Abstract. 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 ..."
Abstract

Cited by 105 (15 self)
 Add to MetaCart
Abstract. 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. 1
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 ..."
Abstract

Cited by 76 (4 self)
 Add to MetaCart
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.
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 ..."
Abstract

Cited by 74 (3 self)
 Add to MetaCart
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. ..."
Abstract

Cited by 68 (20 self)
 Add to MetaCart
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.
A Distributed Algorithm to Evaluate Quantified Boolean Formulae
, 2000
"... In this paper, we present PQSOLVE, a distributed theoremprover for Quantified Boolean Formulae. First, we introduce our sequential algorithm QSOLVE, which uses new heuristics and improves the use of known heuristics to prune the search tree. As a result, QSOLVE is more efficient than the QSAT ..."
Abstract

Cited by 53 (1 self)
 Add to MetaCart
In this paper, we present PQSOLVE, a distributed theoremprover for Quantified Boolean Formulae. First, we introduce our sequential algorithm QSOLVE, which uses new heuristics and improves the use of known heuristics to prune the search tree. As a result, QSOLVE is more efficient than the QSATsolvers previously known. We have parallelized QSOLVE. The resulting distributed QSATsolver PQSOLVE uses parallel search techniques, which we have developed for distributed game tree search. PQSOLVE runs efficiently on distributed systems, i. e. parallel systems without any shared memory. We briefly present experiments that show a speedup of about 114 on 128 processors. To the best of our knowledge we are the first to introduce an efficient parallel QSATsolver.
Beyond NP: ArcConsistency for Quantified Constraints
, 2002
"... The generalization of the satisfiability problem with arbitrary quantifiers is a challenging problem of both theoretical and practical relevance. Being PSPACEcomplete, it provides a canonical model for solving other PSPACE tasks which naturally arise in AI. ..."
Abstract

Cited by 36 (4 self)
 Add to MetaCart
The generalization of the satisfiability problem with arbitrary quantifiers is a challenging problem of both theoretical and practical relevance. Being PSPACEcomplete, it provides a canonical model for solving other PSPACE tasks which naturally arise in AI.
Partial implicit unfolding in the davisputnam procedure for quantified boolean formulae
 In Proceedings of the International Conference on Logic for Programming, Artificial Intelligence and Reasoning (LPAR’01
, 2001
"... Abstract. Quantified Boolean formulae offer a means of representing many propositional formula exponentially more compactly than propositional logic. Recent work on automating reasoning with QBF has concentrated on extending the DavisPutnam procedure to handle QBF. Although the resulting procedures ..."
Abstract

Cited by 33 (0 self)
 Add to MetaCart
Abstract. Quantified Boolean formulae offer a means of representing many propositional formula exponentially more compactly than propositional logic. Recent work on automating reasoning with QBF has concentrated on extending the DavisPutnam procedure to handle QBF. Although the resulting procedures make it possible to evaluate QBF that could not be efficiently reduced to propositional logic (requiring worstcase exponential space), its efficiency often lags much behind the reductive approach when the reduction is possible. We attribute this inefficiency to the fact that many of the unit resolution steps possible in the reduced (propositional logic) formula are not performed in the corresponding QBF. To combine the conciseness of the QBF representation and the stronger inferences available in the unquantified representation, we introduce a stronger propagation algorithm for QBF which could be seen as partially unfolding the universal quantification. The algorithm runs in worstcase exponential time, like the reduction of QBF to propositional logic, but needs only polynomial space. By restricting the algorithm the exponential behavior can be avoided while still preserving many of the useful inferences. 1
Symbolic Decision Procedures for QBF
 Proceedings of 10th Int. Conf. on Principles and Practice of Constraint Programming (CP 2004
, 2004
"... Much recent work has gone into adapting techniques that were originally developed for SAT solving to QBF solving. In particular, QBF solvers are often based on SAT solvers. Most competitive QBF solvers are searchbased. In this work we explore an alternative approach to QBF solving, based on symb ..."
Abstract

Cited by 25 (1 self)
 Add to MetaCart
Much recent work has gone into adapting techniques that were originally developed for SAT solving to QBF solving. In particular, QBF solvers are often based on SAT solvers. Most competitive QBF solvers are searchbased. In this work we explore an alternative approach to QBF solving, based on symbolic quantifier elimination. We extend some recent symbolic approaches for SAT solving to symbolic QBF solving, using various decisiondiagram formalisms such as OBDDs and ZDDs. In both approaches, QBF formulas are solved by eliminating all their quantifiers. Our first solver, QMRES, maintains a set of clauses represented by a ZDD and eliminates quantifiers via multiresolution. Our second solver, QBDD, maintains a set of OBDDs, and eliminate quantifier by applying them to the underlying OBDDs. We compare our symbolic solvers to several competitive searchbased solvers. We show that QBDD is not competitive, but QMRES compares favorably with searchbased solvers on various benchmarks consisting of nonrandom formulas.