An Alternative Representation for QBF

Quantified Boolean formulas are a powerful representation that have been used to capture and solve a variety of problems in Artificial Intelligence. While most research has focused on quantified Boolean formulas in prenex normal form (QBF), we explore an alternative representation of quantified Boolean formulas, called Constrained Quantified Formulas (CQF). CQF allows for a more direct representation of many applications. We present complexity results for CQF and for several subclasses of CQF. We have developed a solver, called QRSsat3, for CQF instances at the second level of the polynomial hierarchy. Computational results of QRSsat3 are compared with the results of solvers for quantified Boolean formulas in prenex normal form.

[1]  Klaus Truemper,et al.  An Effective Algorithm for the Futile Questioning Problem , 2005, Journal of Automated Reasoning.

[2]  K. Truemper,et al.  A Solver for Quantied Formula Problem Q-ALL SAT , 2008 .

[3]  Jussi Rintanen,et al.  Constructing Conditional Plans by a Theorem-Prover , 1999, J. Artif. Intell. Res..

[4]  Klaus Truemper,et al.  Learning to Ask Relevant Questions , 1999, Artif. Intell..

[5]  Armando Tacchella,et al.  Quantifier Structure in Search-Based Procedures for QBFs , 2006, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[6]  Bart Selman,et al.  QBF Modeling: Exploiting Player Symmetry for Simplicity and Efficiency , 2006, SAT.

[7]  Stefan Woltran,et al.  Comparing Different Prenexing Strategies for Quantified Boolean Formulas , 2003, SAT.

[8]  Armando Tacchella,et al.  Learning for quantified boolean logic satisfiability , 2002, AAAI/IAAI.

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

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

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

[12]  Marco Benedetti,et al.  QCSP Made Practical by Virtue of Restricted Quantification , 2007, IJCAI.

[13]  Robert E. Tarjan,et al.  A Linear-Time Algorithm for Testing the Truth of Certain Quantified Boolean Formulas , 1979, Inf. Process. Lett..

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

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

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