Shortening QBF Proofs with Dependency Schemes

Blinkhorn, Joshua; Beyersdorff, Olaf

doi:10.1007/978-3-319-66263-3_17

Cited by 13 publications

(8 citation statements)

References 30 publications

(33 reference statements)

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“…Third, by keeping long-distance Q-resolution as the underlying proof system, QCDCL with dependency learning is amenable to a simple correctness proof and enjoys linear-time strategy extraction. Blinkhorn and Beyersdorff (2017) offered a strong proof-theoretic argument in favor QCDCL with dependency schemes over "vanilla" QCDCL by proving an exponential separation of Q(D rrs )-resolution and ordinary Q-resolution, where Q(D rrs )-resolution is the proof system used by QCDCL with the reflexive resolution-path dependency scheme D rrs and a form of constraint learning that avoids long-distance resolution (e.g. Lonsing, Egly, & Van Gelder, 2013).…”

Section: Discussionmentioning

confidence: 99%

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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Section: Discussionmentioning

confidence: 99%

Dependency Learning for QBF

Peitl¹,

Slivovsky²,

Szeider³

2019

jair

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“…A number of solutions have been proposed for the second problem, most of which are subsumed by the application of dependency schemes [17]. While the use of dependency schemes can speed up solving times [2] and has the potential to dramatically decrease proof sizes in some cases [4], it has distinct disadvantages, such as the fact that it changes the underlying proof system and thus complicates strategy extraction.…”

Section: Prenex Conjunctive Normal Form (Pcnf) the Default Encoding mentioning

confidence: 99%

Qute in the QBF Evaluation 2018

Peitl

Slivovsky

Szeider

2019

SAT

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Qute is a solver for Quantified Boolean Formulas (QBFs) based on Quantified Conflict-Driven Constraint Learning (QCDCL). Its main distinguishing feature is dependency learning, a lazy technique for relaxing restrictions on the order of variable assignments imposed by nested quantifiers. In this short note, we describe the configurations of Qute submitted to QBFEval'18, along with the parameter tuning process that went into creating them.

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“…In general, a dependency scheme allows to exploit independence of certain variables in order to strengthen the universal reduction rule in Q-resolution. Exploiting independence by dependency schemes and related concepts was explored in practical work on solving [29] and in theoretical work on QBF proof complexity [6].…”

Section: Overviewmentioning

confidence: 99%

“…The variant of DepQBF we submitted to QBFEVAL'18 is based on version 6.03 [23]. Compared to previous versions, version 6.03 comes with an advanced technique for cube learning [19] by tightly integrating blocked clause elimination [5,10] into the QCDCL workflow. Thereby, the goal is to dynamically and temporarily remove clauses that are redundant in the current search context.…”

Section: Overviewmentioning

confidence: 99%

QBFRelay, QRATPre+, and DepQBF: Incremental Preprocessing Meets Search-Based QBF Solving

Lonsing

2019

SAT

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DepQBF is a search-based quantified Boolean formula (QBF) solver implementing the QCDCL paradigm. We submitted DepQBF as part of several tool packages to the QBFEVAL'18 competition, which was part of the FLoC Olympic Games 2018. These packages integrate DepQBF as a back end QBF solver and a preprocessing front end called QBFRelay. This front end consists of a shell script that runs several preprocessors in multiple rounds on a given QBF, thus resulting in incremental preprocessing. QBFRelay employs publicly available preprocessors developed by the QBF community and, additionally, our novel preprocessor QRATPre + that is based on a generalization of the QRAT proof system. We present an overview of DepQBF, QRATPre + , and QBFRelay and report on the performance of our submissions, which were awarded a medal in the FLoC Olympic Games.

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Shortening QBF Proofs with Dependency Schemes

Cited by 13 publications

References 30 publications

Dependency Learning for QBF

Dependency Learning for QBF

Qute in the QBF Evaluation 2018

QBFRelay, QRATPre+, and DepQBF: Incremental Preprocessing Meets Search-Based QBF Solving

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