Binary Clause Reasoning in QBF

Binary clause reasoning has found some successful applications in SAT, and it is natural to investigate its use in various extensions of SAT. In this paper we investigate the use of binary clause reasoning in the context of solving Quantified Boolean Formulas (QBF). We develop a DPLL based QBF solver that employs extended binary clause reasoning (hyper-binary resolution) to infer new binary clauses both before and during search. These binary clauses are used to discover additional forced literals, as well as to perform equality reduction. Both of these transformations simplify the theory by removing one of its variables. When applied during DPLL search this stronger inference can offer significant decreases in the size of the search tree, but it can also be costly to apply. We are able to show empirically that despite the extra costs, binary clause reasoning can improve our ability to solve QBF.

[1]  Allen Van Gelder,et al.  Satisfiability testing with more reasoning and less guessing , 1995, Cliques, Coloring, and Satisfiability.

[2]  Fahiem Bacchus,et al.  Enhancing Davis Putnam with extended binary clause reasoning , 2002, AAAI/IAAI.

[3]  Sharad Malik,et al.  Towards a symmetric treatment of satisfaction and conflicts in QBF , 2002 .

[4]  Fahiem Bacchus,et al.  Preprocessing QBF , 2006, CP.

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

[6]  Fahiem Bacchus,et al.  Using SAT in QBF , 2005, CP.

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

[8]  Marco Benedetti,et al.  a QBF decision procedure based on Propositional Skolemization and Symbolic Reasoning , 2004 .

[9]  Marco Benedetti.  a QBF decision procedure based on Propositional Skolemization and Symbolic Reasoning , 2004 .

[10]  Sharad Malik,et al.  Efficient conflict driven learning in a Boolean satisfiability solver , 2001, IEEE/ACM International Conference on Computer Aided Design. ICCAD 2001. IEEE/ACM Digest of Technical Papers (Cat. No.01CH37281).

[11]  Fahiem Bacchus,et al.  Effective Preprocessing with Hyper-Resolution and Equality Reduction , 2003, SAT.

[12]  Armando Tacchella,et al.  QUBE: A System for Deciding Quantified Boolean Formulas Satisfiability , 2001, IJCAR.

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

[14]  Chengqi Zhang,et al.  Association Rule Mining , 2002, Lecture Notes in Computer Science.