On Q-Resolution and CDCL QBF Solving

Janota, Mikoláš

doi:10.1007/978-3-319-40970-2_25

Cited by 22 publications

(28 citation statements)

References 22 publications

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“…This way, the state of the art of QCDCL solving can be further advanced. A related open problem is the inability of plain QCDCL to exploit the full power of Q-resolution [16]. The workflow of QCDCL with generalized axioms is not tailored towards DepQBF 6.0 but can be implemented in any QCDCL solver.…”

Section: Resultsmentioning

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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Section: Resultsmentioning

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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“…Additional experiments show that the number of dependencies learned by Qute on PCNF instances preprocessed by HQSPre (Wimmer et al, 2017) is typically only a fraction of those identified by the standard dependency scheme and even the (reflexive) resolutionpath dependency scheme, and that Qute can deal with formulas that are provably hard to solve for vanilla QCDCL (Janota, 2016). We explain the latter result by formally proving that QCDCL with dependency schemes can solve these formulas in polynomial time.…”

Section: Introductionmentioning

confidence: 87%

“…In a second experiment, we computed the dependency sets given by the standard dependency scheme (Samer & Szeider, 2009;Biere & Lonsing, 2009) and the reflexive resolution-path dependency scheme (Van Gelder, 2011; for preprocessed instances, and compared their sizes to the number of dependencies learned by Qute. Finally, we revisit an instance family which is known to be hard to solve for QCDCL (Janota, 2016) and show they pose no challenge to Qute. In fact, we reinforce the last experimental result by a formal proof that QCDCL with dependency learning can indeed solve instances from this family efficiently.…”

Section: Methodsmentioning

confidence: 99%

“…One of the main obstacles in lifting CDCL to QSAT is that the alternation of existential and universal quantifiers in the quantifier prefix of a QBF (we consider formulas in prenex normal form) introduces dependencies among variables that have to be respected by the order of variable assignments. The resulting constraints not only reduce the empirical effectiveness of branching heuristics but impose severe theoretical limits on the power of QCDCL (Janota, 2016). By default, QCDCL only considers variables from the outermost quantifier block with unassigned variables for branching.…”

Section: Introductionmentioning

confidence: 99%

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Dependency Learning for QBF

Peitl¹,

Slivovsky²,

Szeider³

2019

jair

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Quantified Boolean Formulas (QBFs) can be used to succinctly encode problems from domains such as formal verification, planning, and synthesis. One of the main approaches to QBF solving is Quantified Conflict Driven Clause Learning (QCDCL). By default, QCDCL assigns variables in the order of their appearance in the quantifier prefix so as to account for dependencies among variables. Dependency schemes can be used to relax this restriction and exploit independence among variables in certain cases, but only at the cost of nontrivial interferences with the proof system underlying QCDCL. We introduce dependency learning, a new technique for exploiting variable independence within QCDCL that allows solvers to learn variable dependencies on the fly. The resulting version of QCDCL enjoys improved propagation and increased flexibility in choosing variables for branching while retaining ordinary (long-distance) Q-resolution as its underlying proof system. We show that dependency learning can achieve exponential speedups over ordinary QCDCL. Experiments on standard benchmark sets demonstrate the effectiveness of this technique.

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“…The literature on QCDCL (e.g., [2], [3]) is missing a precise formalization too. In [12] the focus is on the relation of QCDCL with Q-resolution instead of capturing the search precisely.…”

Section: Introductionmentioning

confidence: 99%

A Duality-Aware Calculus for Quantified Boolean Formulas

Fazekas

Seidl

Biere

2016

2016 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)

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Learning and backjumping are essential features in search-based decision procedures for Quantified Boolean Formulas (QBF). To obtain a better understanding of such procedures, we present a formal framework, which allows to simultaneously reason on prenex conjunctive and disjunctive normal form. It captures both satisfying and falsifying search states in a symmetric way. This symmetry simplifies the framework and offers potential for further variants.

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On Q-Resolution and CDCL QBF Solving

Cited by 22 publications

References 22 publications

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

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

Dependency Learning for QBF

A Duality-Aware Calculus for Quantified Boolean Formulas

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