HQSpre - An Effective Preprocessor for QBF and DQBF

We present our new preprocessor HQSpre, a state-of-the-art tool for simplifying quantified Boolean formulas (QBFs) and the first available preprocessor for dependency quantified Boolean formulas (DQBFs). The latter are a generalization of QBFs, resulting from adding so-called Henkin-quantifiers to QBFs. HQSpre applies most of the preprocessing techniques that have been proposed in the literature. It can be used both as a standalone tool and as a library. It is possible to tailor it towards different solver back-ends, e. g., to preserve the circuit structure of the formula when a non-CNF solver back-end is used. Extensive experiments show that HQSpre allows QBF solvers to solve more benchmark instances and is able to decide more instances on its own than state-of-the-art tools. The same impact can be observed in the DQBF domain as well.

[1]  Lakhdar Sais,et al.  Vivifying Propositional Clausal Formulae , 2008, ECAI.

[2]  David A. Plaisted,et al.  A Structure-Preserving Clause Form Translation , 1986, J. Symb. Comput..

[3]  Ilkka Niemelä,et al.  Planning as satisfiability: parallel plans and algorithms for plan search , 2006, Artif. Intell..

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

[5]  Bernd Becker,et al.  Solving DQBF through quantifier elimination , 2015, 2015 Design, Automation & Test in Europe Conference & Exhibition (DATE).

[6]  Chu Min Li,et al.  Heuristics Based on Unit Propagation for Satisfiability Problems , 1997, IJCAI.

[7]  Albert R. Meyer,et al.  Word problems requiring exponential time(Preliminary Report) , 1973, STOC.

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

[9]  Alvaro del Val.  Simplifying Binary Propositional Theories into Connected Components Twice as Fast , 2001, LPAR.

[10]  Bernd Finkbeiner,et al.  Fast DQBF Refutation , 2014, SAT.

[11]  Rolf Drechsler,et al.  A Highly Fault-Efficient SAT-Based ATPG Flow , 2012, IEEE Design & Test of Computers.

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

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

[14]  Christoph Scholl,et al.  An AIG-based QBF-solver using SAT for preprocessing , 2010, Design Automation Conference.

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

[16]  Bernd Becker,et al.  Equivalence checking of partial designs using dependency quantified Boolean formulae , 2013, 2013 IEEE 31st International Conference on Computer Design (ICCD).

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

[18]  G. S. Tseitin.  On the Complexity of Derivation in Propositional Calculus , 1983 .

[19]  Armin Biere,et al.  Bounded model checking , 2003, Adv. Comput..

[20]  Bernd Becker,et al.  Preprocessing for DQBF , 2015, SAT.

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

[22]  Bernd Becker,et al.  Dependency Schemes for DQBF , 2016, SAT.

[23]  Toby Walsh,et al.  Handbook of Satisfiability: Volume 185 Frontiers in Artificial Intelligence and Applications , 2009 .

[24]  J. Reif,et al.  Lower bounds for multiplayer noncooperative games of incomplete information , 2001 .

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

[26]  Armin Biere,et al.  Effective Preprocessing in SAT Through Variable and Clause Elimination , 2005, SAT.

[27]  Enrico Giunchiglia,et al.  sQueezeBF: An Effective Preprocessor for QBFs Based on Equivalence Reasoning , 2010, SAT.

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

[29]  Jie-Hong Roland Jiang,et al.  Henkin quantifiers and Boolean formulae: A certification perspective of DQBF , 2014, Theor. Comput. Sci..

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

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

[32]  Christoph Scholl,et al.  Exploiting structure in an AIG based QBF solver , 2009, 2009 Design, Automation & Test in Europe Conference & Exhibition.

[33]  Bernd Becker,et al.  Incremental preprocessing methods for use in BMC , 2011, Formal Methods Syst. Des..

[34]  Martina Seidl,et al.  SAT-Based Synthesis Methods for Safety Specs , 2014, VMCAI.

[35]  Armin Biere,et al.  Blocked Clause Elimination , 2010, TACAS.

[36]  Helmut Veith,et al.  iDQ: Instantiation-Based DQBF Solving , 2014, POS@SAT.

[37]  Bernd Becker,et al.  Checking equivalence for partial implementations , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).