Unified QBF certification and its applications

  • Authors:

  • Valeriy Balabanov;Jie-Hong R. Jiang

  • Affiliations:

  • Graduate Institute of Electronics Engineering, National Taiwan University, Taipei, Taiwan 10617;Department of Electrical Engineering/Graduate Institute of Electronics Engineering, National Taiwan University, Taipei, Taiwan 10617

  • Venue:
  • Formal Methods in System Design
  • Year:
  • 2012

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Abstract

Quantified Boolean formulae (QBF) allow compact encoding of many decision problems. Their importance motivated the development of fast QBF solvers. Certifying the results of a QBF solver not only ensures correctness, but also enables certain synthesis and verification tasks. To date the certificate of a true formula can be in the form of either a syntactic cube-resolution proof or a semantic Skolem-function model whereas that of a false formula is only in the form of a syntactic clause-resolution proof. The semantic certificate for a false QBF is missing, and the syntactic and semantic certificates are somewhat unrelated. This paper identifies the missing Herbrand-function countermodel for false QBF, and strengthens the connection between syntactic and semantic certificates by showing that, given a true QBF, its Skolem-function model is derivable from its cube-resolution proof of satisfiability as well as from its clause-resolution proof of unsatisfiability under formula negation. Consequently Skolem-function derivation can be decoupled from special Skolemization-based solvers and computed from standard search-based ones. Experimental results show strong benefits of the new method.