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

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.

[1]  Mikolás Janota,et al.  Solving QBF by Clause Selection , 2015, IJCAI.

[2]  Armin Biere,et al.  Resolve and Expand , 2004, SAT.

[3]  Stefan Szeider,et al.  Computing Resolution-Path Dependencies in Linear Time , , 2012, SAT.

[4]  Jie-Hong Roland Jiang,et al.  Unified QBF certification and its applications , 2012, Formal Methods Syst. Des..

[5]  Luca Pulina.  The Ninth QBF Solvers Evaluation - Preliminary Report , 2016, QBF@SAT.

[6]  Armin Biere,et al.  Resolution-Based Certificate Extraction for QBF - (Tool Presentation) , 2012, SAT.

[7]  Stefan Szeider,et al.  Soundness of Q-resolution with dependency schemes , 2016, Theor. Comput. Sci..

[8]  Helmut Veith,et al.  Counterexample-guided abstraction refinement for symbolic model checking , 2003, JACM.

[9]  Markus N. Rabe,et al.  CAQE: A Certifying QBF Solver , 2015, 2015 Formal Methods in Computer-Aided Design (FMCAD).

[10]  Mikolás Janota,et al.  Solving QBF with Counterexample Guided Refinement , 2012, SAT.

[11]  Mikolás Janota,et al.  Proof Complexity of Resolution-based QBF Calculi , 2015, STACS.

[12]  Bernd Becker,et al.  Verification of partial designs using incremental QBF solving , 2012, 2012 Design, Automation & Test in Europe Conference & Exhibition (DATE).

[13]  Reinhold Letz,et al.  Lemma and Model Caching in Decision Procedures for Quantified Boolean Formulas , 2002, TABLEAUX.

[14]  Inês Lynce,et al.  Conflict-Driven Clause Learning SAT Solvers , 2009, Handbook of Satisfiability.

[15]  Florian Lonsing,et al.  The QBF Gallery: Behind the scenes , 2016, Artif. Intell..

[16]  Armin Biere,et al.  Enhancing Search-Based QBF Solving by Dynamic Blocked Clause Elimination , 2015, LPAR.

[17]  Mikolás Janota,et al.  On Q-Resolution and CDCL QBF Solving , 2016, SAT.

[18]  Christoph Scholl,et al.  The QBF Solver AIGSolve , 2016, QBF@SAT.

[19]  Armin Biere,et al.  Blocked Clause Elimination for QBF , 2011, CADE.

[20]  Florian Lonsing,et al.  Q-Resolution with Generalized Axioms , 2016, SAT.

[21]  J. A. Robinson,et al.  A Machine-Oriented Logic Based on the Resolution Principle , 1965, JACM.

[22]  Marco Schaerf,et al.  An Algorithm to Evaluate Quantified Boolean Formulae , 1998, AAAI/IAAI.

[23]  Florian Lonsing,et al.  Long-Distance Resolution: Proof Generation and Strategy Extraction in Search-Based QBF Solving , 2013, LPAR.

[24]  Bernd Becker,et al.  HQSpre - An Effective Preprocessor for QBF and DQBF , 2017, TACAS.

[25]  Hans Kleine Büning,et al.  Bounded Universal Expansion for Preprocessing QBF , 2007, SAT.

[26]  David A. Basin,et al.  QUBOS: Deciding Quantified Boolean Logic Using Propositional Satisfiability Solvers , 2002, FMCAD.

[27]  Armin Biere,et al.  DepQBF: A Dependency-Aware QBF Solver , 2010, J. Satisf. Boolean Model. Comput..

[28]  Oliver Kullmann,et al.  On a Generalization of Extended Resolution , 1999, Discret. Appl. Math..

[29]  Armin Biere,et al.  Integrating Dependency Schemes in Search-Based QBF Solvers , 2010, SAT.

[30]  Donald W. Loveland,et al.  A machine program for theorem-proving , 2011, CACM.

[31]  Armin Biere,et al.  Clause Elimination for SAT and QSAT , 2015, J. Artif. Intell. Res..

[32]  Hans Kleine Büning,et al.  Theory of Quantified Boolean Formulas , 2021, Handbook of Satisfiability.

[33]  Luca Pulina,et al.  Twelve Years of QBF Evaluations: QSAT Is PSPACE-Hard and It Shows , 2016, Fundam. Informaticae.

[34]  Florian Lonsing,et al.  Efficient Clause Learning for Quantified Boolean Formulas via QBF Pseudo Unit Propagation , 2013, SAT.

[35]  Hans Kleine Büning,et al.  Resolution for Quantified Boolean Formulas , 1995, Inf. Comput..

[36]  Shahab Tasharrofi,et al.  SAT-to-SAT in QBFEval 2016 , 2016, QBF@SAT.

[37]  Armando Tacchella,et al.  Clause/Term Resolution and Learning in the Evaluation of Quantified Boolean Formulas , 2006, J. Artif. Intell. Res..

[38]  Florian Lonsing,et al.  Evaluating QBF Solvers: Quantifier Alternations Matter , 2018, CP.

[39]  Sharad Malik,et al.  Towards a Symmetric Treatment of Satisfaction and Conflicts in Quantified Boolean Formula Evaluation , 2002, CP.

[40]  Sharad Malik,et al.  Conflict driven learning in a quantified Boolean Satisfiability solver , 2002, ICCAD 2002.

[41]  Allen Van Gelder.  Variable Independence and Resolution Paths for Quantified Boolean Formulas , 2011, CP.

[42]  Florian Lonsing,et al.  Conformant planning as a case study of incremental QBF solving , 2016, Annals of Mathematics and Artificial Intelligence.

[43]  Edmund M. Clarke,et al.  A Non-prenex, Non-clausal QBF Solver with Game-State Learning , 2010, SAT.

[44]  Marko Samer,et al.  Backdoor Sets of Quantified Boolean Formulas , 2008, Journal of Automated Reasoning.

[45]  Florian Lonsing,et al.  Incremental QBF Solving , 2014, CP.

[46]  Olaf Beyersdorff,et al.  Dependency Schemes in QBF Calculi: Semantics and Soundness , 2016, QBF@SAT.

[47]  Florian Lonsing,et al.  Incrementally Computing Minimal Unsatisfiable Cores of QBFs via a Clause Group Solver API , 2015, SAT.

[48]  Jie-Hong Roland Jiang,et al.  QBF Resolution Systems and Their Proof Complexities , 2014, SAT.

[49]  Allen Van Gelder.  Contributions to the Theory of Practical Quantified Boolean Formula Solving , 2012, CP.

[50]  Mikolás Janota,et al.  Expansion-based QBF solving versus Q-resolution , 2015, Theor. Comput. Sci..