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Efficient Preprocessing Methods for Quantifier Elimination

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Computer Algebra in Scientific Computing (CASC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4194))

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Abstract

This paper presents a framework and prototype implementation for preprocessing quantified input formulas that are intended as input for quantifier elimination algorithms. The framework loosely follows the AI search paradigm — exploring the space of formulas derived from the input by applying various rewriting operators in search of a problem formulation that will be good input for the intended Q.E. program. The only operator provided by the prototype implementation presented here is substitution for variables constrained by equations in which they appear linearly, supported by factorization and a simple check for non-vanishing of denominators in substitutions. Yet we present examples of quantified formulas which can be reduced by our preprocessing method to problems solvable by current quantifier elimination packages, whereas the original formulas had been inaccessible to those.

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Author information

Authors and Affiliations

  1. Department of Computer Science, United States Naval Academy, U.S.A.

    Christopher W. Brown

  2. Institut für Informatik II, Universität Bonn, Römerstr. 164, 53117, Bonn, Germany

    Christian Gross

Authors
  1. Christopher W. Brown
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  2. Christian Gross
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Editor information

Editors and Affiliations

  1. Institute of Informatics, Technische Universität München, Boltzmannstr. 3, 85748, Garching, Germany

    Victor G. Ganzha  & Ernst W. Mayr  & 

  2. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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© 2006 Springer-Verlag Berlin Heidelberg

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Brown, C.W., Gross, C. (2006). Efficient Preprocessing Methods for Quantifier Elimination. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2006. Lecture Notes in Computer Science, vol 4194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11870814_7

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  • DOI: https://doi.org/10.1007/11870814_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-45182-2

  • Online ISBN: 978-3-540-45195-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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