Shortening QBF Proofs with Dependency Schemes

Integrating Dependency Schemes in Search-Based QBF Solvers

Theory and Applications of Satisfiability Testing – SAT 2010 - Lecture Notes in Computer Science ◽

10.1007/978-3-642-14186-7_14 ◽

2010 ◽

pp. 158-171 ◽

Cited By ~ 25

Author(s):

Florian Lonsing ◽

Armin Biere

Keyword(s):

Dependency Schemes

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Chapter 31. Quantified Boolean Formulas

Frontiers in Artificial Intelligence and Applications - Handbook of Satisfiability ◽

10.3233/faia201015 ◽

2021 ◽

Author(s):

Olaf Beyersdorff ◽

Mikoláš Janota ◽

Florian Lonsing ◽

Martina Seidl

Keyword(s):

Performance Characteristics ◽

Proof Complexity ◽

Proof Systems ◽

Quantified Boolean Formulas ◽

Boolean Formulas ◽

Clause Learning ◽

Dependency Schemes

Solvers for quantified Boolean formulas (QBF) have become powerful tools for tackling hard computational problems from various application domains, even beyond the scope of SAT. This chapter gives a description of the main algorithmic paradigms for QBF solving, including quantified conflict driven clause learning (QCDCL), expansion-based solving, dependency schemes, and QBF preprocessing. Particular emphasis is laid on the connections of these solving approaches to QBF proof systems: Q-Resolution and its variants in the case of QCDCL, expansion QBF resolution calculi for expansion-based solving, and QRAT for preprocessing. The chapter also surveys the relations between the various QBF proof systems and results on their proof complexity, thereby shedding light on the diverse performance characteristics of different solving approaches that are observed in practice.

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Long-Distance Q-Resolution with Dependency Schemes

Journal of Automated Reasoning ◽

10.1007/s10817-018-9467-3 ◽

2018 ◽

Vol 63 (1) ◽

pp. 127-155 ◽

Cited By ~ 3

Author(s):

Tomáš Peitl ◽

Friedrich Slivovsky ◽

Stefan Szeider

Keyword(s):

Long Distance ◽

Dependency Schemes

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Dependency Learning for QBF

Journal of Artificial Intelligence Research ◽

10.1613/jair.1.11529 ◽

2019 ◽

Vol 65 ◽

pp. 181-208 ◽

Cited By ~ 4

Author(s):

Tomáš Peitl ◽

Friedrich Slivovsky ◽

Stefan Szeider

Keyword(s):

Formal Verification ◽

New Technique ◽

Proof System ◽

Long Distance ◽

Quantified Boolean Formulas ◽

Boolean Formulas ◽

Clause Learning ◽

A New Technique ◽

The Cost ◽

Dependency Schemes

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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