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A solver for QBFs in negation normal form

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Abstract

Various problems in artificial intelligence can be solved by translating them into a quantified boolean formula (QBF) and evaluating the resulting encoding. In this approach, a QBF solver is used as a black box in a rapid implementation of a more general reasoning system. Most of the current solvers for QBFs require formulas in prenex conjunctive normal form as input, which makes a further translation necessary, since the encodings are usually not in a specific normal form. This additional step increases the number of variables in the formula or disrupts the formula’s structure. Moreover, the most important part of this transformation, prenexing, is not deterministic. In this paper, we focus on an alternative way to process QBFs without these drawbacks and describe a solver, \(\ensuremath{\sf qpro}\), which is able to handle arbitrary formulas. To this end, we extend algorithms for QBFs to the non-normal form case and compare \(\ensuremath{\sf qpro}\) with the leading normal form provers on several problems from the area of artificial intelligence. We prove properties of the algorithms generalized to non-clausal form by using a novel approach based on a sequent-style formulation of the calculus.

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Authors and Affiliations

  1. Knowledge-based Systems Group E184/3, Institute of Information Systems, Vienna University of Technology, Favoritenstrasse 9-11, A-1040, Vienna, Austria

    Uwe Egly, Martina Seidl & Stefan Woltran

  2. Business Informatics Group E188/3, Institute of Software Technology and Interactive Systems, Vienna University of Technology, Favoritenstrasse 9-11, 1040, Vienna, Austria

    Martina Seidl

  3. Database and Artificial Intelligence Group E184/2, Institute of Information Systems, Vienna University of Technology, Favoritenstrasse 9-11, A-1040, Vienna, Austria

    Stefan Woltran

Authors
  1. Uwe Egly
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  2. Martina Seidl
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  3. Stefan Woltran
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Correspondence to Uwe Egly.

Additional information

This paper is based on an extended abstract presented at ECAI 2006 (see [16]). This work was supported by the Austrian Science Fund (FWF) under grant P18019, the Austrian Academic Exchange Service (ÖAD) under grant Amadée 2/2006, and by the Austrian Federal Ministry of Transport, Innovation and Technology BMVIT and the Austrian Research Promotion Agency FFG under grant FIT-IT-810806.

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Egly, U., Seidl, M. & Woltran, S. A solver for QBFs in negation normal form. Constraints 14, 38–79 (2009). https://doi.org/10.1007/s10601-008-9055-y

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