Resolution-Based Certificate Extraction for QBF

Niemetz, Aina; Preiner, Mathias; Lonsing, Florian; Seidl, Martina; Biere, Armin

doi:10.1007/978-3-642-31612-8_33

Cited by 51 publications

(44 citation statements)

References 6 publications

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“…QPUP learning is applied to the original formula as well as to the guard formula. It is compatible with all the sophisticated techniques already in DepQBF, including pure literal detection, proof generation for certificate extraction [1,13], and the standard dependency scheme.…”

Section: Resultsmentioning

confidence: 99%

“…If E in case 3 is an empty clause, the truth value of Ψ can be proven to be true. It is straightforward in principle to extract either Q-refutation from a trace of the solver's actions [1,13]. If G in case 1 is an empty clause, the truth value of Ψ can be shown to be true simply by applying the hitting set underlying G to Ψ , because the hitting set contains only existential variables (based on − → Q ).…”

Section: Qcdcl Terminating Eventsmentioning

confidence: 99%

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Efficient Clause Learning for Quantified Boolean Formulas via QBF Pseudo Unit Propagation

Lonsing

Egly

Gelder

2013

Theory and Applications of Satisfiability Testing – SAT 2013

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Abstract. Recent solvers for quantified boolean formulas (QBF) use a clause learning method based on a procedure proposed by Giunchiglia et al. (JAIR 2006), which avoids creating tautological clauses. Recently, an exponential worst case for this procedure has been shown by Van Gelder (CP 2012). That paper introduced QBF Pseudo Unit Propagation (QPUP) for non-tautological clause learning in a limited setting and showed that its worst case is theoretically polynomial, although it might be impractical in a high-performance QBF solver, due to excessive time and space consumption. No implementation was reported. We describe an enhanced version of QPUP learning that is practical to incorporate into high-performance QBF solvers, being compatible with pure-literal rules and dependency schemes. It can be used for proving in a concise format that a QBF formula is either unsatisfiable or satisfiable (working on both proofs in tandem). A lazy version of QPUP permits non-tautological clauses to be learned without actually carrying out resolutions, but this version is unable to produce proofs. Experimental results show that QPUP is somewhat faster than the previous nontautological clause learning procedure on benchmarks from QBFEVAL-12-SR.

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Section: Resultsmentioning

confidence: 99%

Section: Qcdcl Terminating Eventsmentioning

confidence: 99%

Efficient Clause Learning for Quantified Boolean Formulas via QBF Pseudo Unit Propagation

Lonsing

Egly

Gelder

2013

Theory and Applications of Satisfiability Testing – SAT 2013

Self Cite

View full text Add to dashboard Cite

show abstract

“…Third, our proof system can simulate universal expansion and other existing techniques. Future work will focus on rewriting search based QBF solver techniques [18] to the QRAT proof system and extracting Skolem functions [4] from QRAT proofs.…”

Section: Resultsmentioning

confidence: 99%

“…Effectively checking the result returned by a QBF solver has been an open challenge for a long time [1,2,3,4,5,6,7]. The current state-of-the-art is to simply dump Q-resolution proofs and to validate their structure.…”

Section: Introductionmentioning

confidence: 99%

A Unified Proof System for QBF Preprocessing

Heule

Seidl²,

Biere³

2014

Automated Reasoning

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Abstract. For quantified Boolean formulas (QBFs), preprocessing is essential to solve many real-world formulas. The application of a preprocessor, however, prevented the extraction of proofs for the original formula. Such proofs are required to independently validate correctness of the preprocessor's rewritings and the solver's result. Especially for universal expansion proof checking was not possible so far. In this paper, we introduce a unified proof system based on three simple and elegant quantified resolution asymmetric tautology (QRAT) rules. In combination with an extended version of universal reduction, they are sufficient to efficiently express all preprocessing techniques used in state-of-the-art preprocessors including universal expansion. Moreover, these rules give rise to new preprocessing techniques. We equip our preprocessor bloqqer with QRAT proof logging and provide a proof checker for QRAT proofs.

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“…Certificate construction in QBF has seen increasing interest in recent research [8,12,18,19,21,30,36,37]. While providing certificates is not implemented in our prototype yet, our architecture can easily be extended by this feature.…”

Section: Resultsmentioning

confidence: 99%

iDQ: Instantiation-Based DQBF Solving

Fröhlich¹,

Kovásznai²,

Biere³

et al.

EPiC Series in Computing

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Dependency Quantified Boolean Formulas (DQBF) are obtained by adding Henkin quantifiers to Boolean formulas and have seen growing interest in the last years. Since deciding DQBF is NExpTime-complete, efficient ways of solving it would have many practical applications. Still, there is only few work on solving this kind of formulas in practice. In this paper, we present an instantiation-based technique to solve DQBF efficiently. Apart from providing a theoretical foundation, we also propose a concrete implementation of our algorithm. Finally, we give a detailed experimental analysis evaluating our prototype iDQ on several DQBF as well as QBF benchmarks.

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Resolution-Based Certificate Extraction for QBF

Cited by 51 publications

References 6 publications

Efficient Clause Learning for Quantified Boolean Formulas via QBF Pseudo Unit Propagation

Efficient Clause Learning for Quantified Boolean Formulas via QBF Pseudo Unit Propagation

A Unified Proof System for QBF Preprocessing

iDQ: Instantiation-Based DQBF Solving

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