Solving Quantified Boolean Formulas with Circuit Observability Don’t Cares

  • Daijue Tang
  • Sharad Malik
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4121)


Traditionally the propositional part of a Quantified Boolean Formula (QBF) instance has been represented using a conjunctive normal form (CNF). As with propositional satisfiability (SAT), this is motivated by the efficiency of this data structure. However, in many cases, part of or the entire propositional part of a QBF instance can often be represented as a combinational logic circuit. In a logic circuit, the limited observability of the internal signals at the circuit outputs may make their assignments irrelevant for specific assignments of values to other signals in the circuit. This circuit observability don’t care (ODC) information has been used to advantage in circuit based SAT solvers. A CNF encoding of the circuit, however, does not capture the signal direction and this limited observability, and thus cannot directly take advantage of this. However, recently it has been shown that this don’t care information can be encoded in the CNF description and taken advantage of in a DPLL based SAT solver by modifying the decision heuristics/Boolean constraint propagation/conflict-driven-learning to account for these don’t cares. Thus far, however, the use of these don’t cares in the CNF encoding has not been explored for QBF solvers. In this paper, we examine how this can be done for QBF solvers as well as evaluate its practical benefits through experimentation. We have developed and implemented the usage of circuit ODCs in various parts of the DPLL-based procedure of the Quaffle QBF solver. We show that DPLL search based QBF solvers can use circuit ODC information to detect satisfying branches earlier during search and make satisfiability directed learning more effective. Our experiments demonstrate that significant performance gain can be obtained by considering circuit ODCs in checking the satisfiability of QBFs.


Boolean Function Boolean Formula Propositional Formula Satisfying Assignment Partial Assignment 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Daijue Tang
    • 1
  • Sharad Malik
    • 1
  1. 1.Princeton UniversityPrincetonUSA

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