Towards a Symmetric Treatment of Satisfaction and Conflicts in Quantified Boolean Formula Evaluation

  • Lintao Zhang
  • Sharad Malik
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2470)

Abstract

In this paper, we describe a new framework for evaluating Quantified Boolean Formulas (QBF). The new framework is based on the Davis-Putnam (DPLL) search algorithm. In existing DPLL based QBF algorithms, the problem database is represented in Conjunctive Normal Form (CNF) as a set of clauses, implications are generated from these clauses, and backtracking in the search tree is chronological. In this work, we augment the basic DPLL algorithm with conflict driven learning as well as satisfiability directed implication and learning. In addition to the traditional clause database, we add a cube database to the data structure. We show that cubes can be used to generate satisfiability directed implications similar to conflict directed implications generated by the clauses. We show that in a QBF setting, conflicting leaves and satisfying leaves of the search tree both provide valuable information to the solver in a symmetric way. We have implemented our algorithm in the new QBF solver Quaffle. Experimental results show that for some test cases, satisfiability directed implication and learning significantly prunes the search.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Lintao Zhang
    • 1
  • Sharad Malik
    • 1
  1. 1.Department of Electrical EngineeringPrinceton UniversityPrinceton

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