Incrementally Computing Minimal Unsatisfiable Cores of QBFs via a Clause Group Solver API

Lonsing, Florian; Egly, Uwe

doi:10.1007/978-3-319-24318-4_14

Cited by 5 publications

(5 citation statements)

References 32 publications

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“…Additionally, we also implemented the QMaxHS approach described in Section 3.3. The implementation was done on top of DepQBF 4 , the known QBF solver which is capable or reporting unsatisfiable cores [42]. However, the performance of QMaxHS is poor (i.e.…”

Section: Methodsmentioning

confidence: 99%

“…Given the reduction of propositional abduction to QMaxSAT, any coreguided MaxSAT algorithm can be used, provided a core-producing QBF solver is used [24,42].…”

Section: Abduction With Qmaxsatmentioning

confidence: 99%

“…A straightforward solution for solving QMaxSAT is to replace the SAT oracle by a QBF oracle in MaxHS. This approach is referred to as QMaxHS, and it was implemented on top of DepQBF, the known QBF solver which is capable of reporting unsatisfiable cores if the input QBF is false [42]. It should be noted (and it is also mentioned in Section 4) that the implementation of QMaxHS performs quite bad (it cannot solve any benchmark instances considered in Section 4).…”

Section: Abduction With Qmaxsatmentioning

confidence: 99%

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Propositional Abduction with Implicit Hitting Sets

Ignatiev¹,

Morgado²,

Marques-Silva³

2016

Preprint

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Logic-based abduction finds important applications in artificial intelligence and related areas. One application example is in finding explanations for observed phenomena. Propositional abduction is a restriction of abduction to the propositional domain, and complexity-wise is in the second level of the polynomial hierarchy. Recent work has shown that exploiting implicit hitting sets and propositional satisfiability (SAT) solvers provides an efficient approach for propositional abduction. This paper investigates this earlier work and proposes a number of algorithmic improvements. These improvements are shown to yield exponential reductions in the number of SAT solver calls. More importantly, the experimental results show significant performance improvements compared to the the best approaches for propositional abduction.

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Section: Methodsmentioning

confidence: 99%

“…Given the reduction of propositional abduction to QMaxSAT, any coreguided MaxSAT algorithm can be used, provided a core-producing QBF solver is used [24,42].…”

Section: Abduction With Qmaxsatmentioning

confidence: 99%

Section: Abduction With Qmaxsatmentioning

confidence: 99%

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Propositional Abduction with Implicit Hitting Sets

Ignatiev¹,

Morgado²,

Marques-Silva³

2016

Preprint

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“…The API of DepQBF allows to modify the PCNFs in S by manipulating the quantifier prefix and adding or removing sets of clauses in a stack-based way. Since version 4.0, it is possible to add or remove sets of clauses arbitrarily [29] and to extract unsatisfiable cores, i.e., unsatisfiable subformulas of the PCNF ψ i . At any time when solving ψ i ∈ S, the soundness property of QCDCL (Section 3) that ψ ≡ sat ψ θ and ψ ≡ sat ψ γ , where ψ = ψ i , must hold.…”

Section: Features Of Depqbfmentioning

confidence: 99%

DepQBF 6.0: A Search-Based QBF Solver Beyond Traditional QCDCL

Lonsing

Egly

2017

Lecture Notes in Computer Science

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We present the latest major release version 6.0 of the quantified Boolean formula (QBF) solver DepQBF, which is based on QCDCL. QCDCL is an extension of the conflict-driven clause learning (CDCL) paradigm implemented in state of the art propositional satisfiability (SAT) solvers. The Q-resolution calculus (QRES) is a QBF proof system which underlies QCDCL. QCDCL solvers can produce QRES proofs of QBFs in prenex conjunctive normal form (PCNF) as a byproduct of the solving process. In contrast to traditional QCDCL based on QRES, DepQBF 6.0 implements a variant of QCDCL which is based on a generalization of QRES. This generalization is due to a set of additional axioms and leaves the original Q-resolution rules unchanged. The generalization of QRES enables QCDCL to potentially produce exponentially shorter proofs than the traditional variant. We present an overview of the features implemented in DepQBF and report on experimental results which demonstrate the effectiveness of generalized QRES in QCDCL.Comment: 12 pages + appendix; to appear in the proceedings of CADE-26, LNCS, Springer, 201

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“…Implemented in the state-of-the-art solver DepQBF [15,16], one of the recent and exciting developments in QBF solving has seen the introduction of dependency schemes: algorithms that gather information on variable independence by prior appeal to the syntactic form of an instance. The quantifier prefix of a QBF (in prenex normal form) imposes a total order on the variables; due to the nesting of quantifier scopes, the value of a Boolean variable z can be dependent upon the variables to its left in the prefix.…”

Section: Introductionmentioning

confidence: 99%

Dependency Schemes in QBF Calculi: Semantics and Soundness

Beyersdorff

Blinkhorn

2016

Lecture Notes in Computer Science

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Abstract. We study the parametrisation of QBF resolution calculi by dependency schemes. One of the main problems in this area is to understand for which dependency schemes the resulting calculi are sound. Towards this end we propose a semantic framework for variable independence based on 'exhibition' by QBF models, and use it to express a property of dependency schemes called full exhibition that is known to be sufficient for soundness in Q-resolution. Introducing a generalised form of the long-distance resolution rule, we propose a complete parametrisation of classical long-distance Q-resolution, and show that full exhibition remains sufficient for soundness. We demonstrate that our approach applies to the current research frontiers by proving that the reflexive resolution path dependency scheme is fully exhibited.

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Incrementally Computing Minimal Unsatisfiable Cores of QBFs via a Clause Group Solver API

Cited by 5 publications

References 32 publications

Propositional Abduction with Implicit Hitting Sets

Propositional Abduction with Implicit Hitting Sets

DepQBF 6.0: A Search-Based QBF Solver Beyond Traditional QCDCL

Dependency Schemes in QBF Calculi: Semantics and Soundness

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