Solving QBF by Clause Selection

Algorithms based on the enumeration of implicit hitting sets find a growing number of applications, which include maximum satisfiability and model based diagnosis, among others. This paper exploits enumeration of implicit hitting sets in the context of Quantified Boolean Formulas (QBF). The paper starts by developing a simple algorithm for QBF with two levels of quantification, which is shown to relate with existing work on enumeration of implicit hitting sets, but also with recent work on QBF based on abstraction refinement. The paper then extends these ideas and develops a novel QBF algorithm, which generalizes the concept of enumeration of implicit hitting sets. Experimental results, obtained on representative problem instances, show that the novel algorithm is competitive with, and often outperforms, the state of the art in QBF solving.

[1]  Sharad Malik,et al.  Conflict driven learning in a quantified Boolean satisfiability solver , 2002, IEEE/ACM International Conference on Computer Aided Design, 2002. ICCAD 2002..

[2]  Lintao Zhang,et al.  Solving QBF by Combining Conjunctive and Disjunctive Normal Forms , 2006, AAAI.

[3]  Fahiem Bacchus,et al.  Postponing Optimization to Speed Up MAXSAT Solving , 2013, CP.

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

[5]  Niklas Sörensson,et al.  Temporal induction by incremental SAT solving , 2003, BMC@CAV.

[6]  Lintao Zhang,et al.  Solving QBF with combined conjunctive and disjunctive normal form , 2006, AAAI 2006.

[7]  Niklas Sörensson,et al.  An Extensible SAT-solver , 2003, SAT.

[8]  Armin Biere,et al.  Bridging the gap between dual propagation and CNF-based QBF solving , 2013, 2013 Design, Automation & Test in Europe Conference & Exhibition (DATE).

[9]  Leonid Ryzhyk,et al.  Solving Games without Controllable Predecessor , 2014, CAV.

[10]  Fahiem Bacchus,et al.  Exploiting the Power of mip Solvers in maxsat , 2013, SAT.

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

[12]  Jussi Rintanen,et al.  Improvements to the Evaluation of Quantified Boolean Formulae , 1999, IJCAI.

[13]  Santosh S. Vempala,et al.  Algorithms for implicit hitting set problems , 2011, SODA '11.

[14]  John Slaney.  Set-theoretic duality: A fundamental feature of combinatorial optimisation , 2014, ECAI.

[15]  Mikolás Janota,et al.  Abstraction-Based Algorithm for 2QBF , 2011, SAT.

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

[17]  Marco Benedetti,et al.  QBF-Based Formal Verification: Experience and Perspectives , 2008, J. Satisf. Boolean Model. Comput..

[18]  Karem A. Sakallah,et al.  Algorithms for Computing Minimal Unsatisfiable Subsets of Constraints , 2007, Journal of Automated Reasoning.

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

[20]  Joao Marques-Silva,et al.  Partial MUS Enumeration , 2013, AAAI.

[21]  Bart Selman,et al.  The Achilles' Heel of QBF , 2005, AAAI.

[22]  Enrico Giunchiglia,et al.  Reasoning with Quantified Boolean Formulas , 2021, Handbook of Satisfiability.

[23]  Richard M. Karp,et al.  The Implicit Hitting Set Approach to Solve Combinatorial Optimization Problems with an Application to Multigenome Alignment , 2013, Oper. Res..

[24]  Marco Benedetti,et al.  Evaluating QBFs via Symbolic Skolemization , 2005, LPAR.

[25]  Fahiem Bacchus,et al.  Exploiting QBF Duality on a Circuit Representation , 2010, AAAI.

[26]  Richard M. Karp,et al.  Implicit Hitting Set Problems and Multi-genome Alignment , 2010, CPM.

[27]  Fahiem Bacchus,et al.  A Uniform Approach for Generating Proofs and Strategies for Both True and False QBF Formulas , 2011, IJCAI.

[28]  Raymond Reiter,et al.  A Theory of Diagnosis from First Principles , 1986, Artif. Intell..

[29]  Jussi Rintanen,et al.  Asymptotically Optimal Encodings of Conformant Planning in QBF , 2007, AAAI.

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

[31]  Sharad Malik,et al.  Validating SAT solvers using an independent resolution-based checker: practical implementations and other applications , 2003, 2003 Design, Automation and Test in Europe Conference and Exhibition.

[32]  Meir Kalech,et al.  Exploring the Duality in Conflict-Directed Model-Based Diagnosis , 2012, AAAI.

[33]  Fahiem Bacchus,et al.  Solving MAXSAT by Solving a Sequence of Simpler SAT Instances , 2011, CP.

[34]  Christos H. Papadimitriou,et al.  Computational complexity , 1993 .

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

[36]  Armando Tacchella,et al.  Backjumping for Quantified Boolean Logic satisfiability , 2001, Artif. Intell..