Integrating Dependency Schemes in Search-Based QBF Solvers

Lonsing, Florian; Biere, Armin

doi:10.1007/978-3-642-14186-7_14

Cited by 41 publications

(38 citation statements)

References 26 publications

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“…For QF BV2 bw this shows the importance of bit-width reduction as proposed in [16,17] before bit-blasting. For formulas in QF BV2 31 or one of the related classes, only using shift by 1, addition, multiplication by constant, and indexing, techniques used in state-of-the-art QBF solvers [25] or symbolic model checking on Sequential Circuits [19] might be of interest.…”

Section: Discussionmentioning

confidence: 99%

More on the Complexity of Quantifier-Free Fixed-Size Bit-Vector Logics with Binary Encoding

Fröhlich

Kovásznai

Biere

2013

Computer Science – Theory and Applications

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Abstract. Bit-precise reasoning is important for many practical applications of Satisfiability Modulo Theories (SMT). In recent years, efficient approaches for solving fixed-size bit-vector formulas have been developed. From the theoretical point of view, only few results on the complexity of fixed-size bit-vector logics have been published. Most of these results only hold if unary encoding on the bit-width of bit-vectors is used. In previous work [1], we showed that binary encoding adds more expressiveness to bit-vector logics, e.g. it makes fixed-size bit-vector logic without uninterpreted functions nor quantification NExpTime-complete. In this paper, we look at the quantifier-free case again and propose two new results. While it is enough to consider logics with bitwise operations, equality, and shift by constant to derive NExpTime-completeness, we show that the logic becomes PSpace-complete if, instead of shift by constant, only shift by 1 is permitted, and even NP-complete if no shifts are allowed at all.

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Section: Discussionmentioning

confidence: 99%

More on the Complexity of Quantifier-Free Fixed-Size Bit-Vector Logics with Binary Encoding

Fröhlich

Kovásznai

Biere

2013

Computer Science – Theory and Applications

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“…This policy is implemented in early versions of QuBE. Essentially the same policy is used in depQBF [18,19]. A slight variant is used in CirQit [9,8].…”

Section: Qdpll Exponential Casementioning

confidence: 99%

Contributions to the Theory of Practical Quantified Boolean Formula Solving

Gelder

2012

Lecture Notes in Computer Science

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Abstract. Recent solvers for quantified boolean formulas (QBFs) use a clause learning method based on a procedure proposed by Giunchiglia et al. (JAIR 2006), which avoids creating tautological clauses. The underlying proof system is Q-resolution. This paper shows an exponential worst case for the clause-learning procedure. This finding confirms empirical observations that some formulas take mysteriously long times to solve, compared to other apparently similar formulas. Q-resolution is known to be refutation complete for QBF, but not all logically implied clauses can be derived with it. A stronger proof system called QU-resolution is introduced, and shown to be complete in this stronger sense. A new procedure called QPUP for clause learning without tautologies is also described. A generalization of pure literals is introduced, called effectively depthmonotonic literals. In general, the variable-elimination resolution operation, as used by Quantor, sQueezeBF, and Bloqqer is unsound if the existential variable being eliminated is not at innermost scope. It is shown that variable-elimination resolution is sound for effectively depthmonotonic literals even when they are not at innermost scope.

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“…A dependency scheme is a relation on variables indicating the dependence among them. In QBF standard dependency schemes and related techniques grant QBF solvers more freedom in the solution process [11][12][13] . These techniques have been introduced and integrated in QBF solvers successfully, but in QCSP standard dependency schemes have only been investigated in theory [14] .…”

Section: Introductionmentioning

confidence: 99%

Integrating Standard Dependency Schemes in QCSP Solvers

Jin

Zhang

2012

J. Comput. Sci. Technol.

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Quantified constraint satisfaction problems (QCSPs) are an extension to constraint satisfaction problems (CSPs) with both universal quantifiers and existential quantifiers. In this paper we apply variable ordering heuristics and integrate standard dependency schemes in QCSP solvers. The technique can help to decide the next variable to be assigned in QCSP solving. We also introduce a new factor into the variable ordering heuristics: a variable's dep is the number of variables depending on it. This factor represents the probability of getting more candidates for the next variable to be assigned. Experimental results show that variable ordering heuristics with standard dependency schemes and the new factor dep can improve the performance of QCSP solvers.

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Integrating Dependency Schemes in Search-Based QBF Solvers

Cited by 41 publications

References 26 publications

More on the Complexity of Quantifier-Free Fixed-Size Bit-Vector Logics with Binary Encoding

More on the Complexity of Quantifier-Free Fixed-Size Bit-Vector Logics with Binary Encoding

Contributions to the Theory of Practical Quantified Boolean Formula Solving

Integrating Standard Dependency Schemes in QCSP Solvers

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