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An Effective Implementation of a Special Quantifier Elimination for a Sign Definite Condition by Logical Formula Simplification

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Computer Algebra in Scientific Computing (CASC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8136))

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Abstract

This paper presents an efficient quantifier elimination algorithm tailored for a sign definite condition (SDC). The SDC for a polynomial f ∈ ℝ[x] with parametric coefficients is written as ∀ x ( x ≥ 0 → f(x) > 0). To improve the algorithm, simplification of an output formula is needed. We show a necessary condition for the SDC and an approach to simplify formulae by using a logic minimization method. Experimental results show that our approach significantly simplify formulae.

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Author information

Authors and Affiliations

  1. IT Systems Laboratories, Fujitsu Laboratories Ltd., Kamikodanaka 4-1-1, Nakahara-ku, Kawasaki, 211-8588, Japan

    Hidenao Iwane, Hiroyuki Higuchi & Hirokazu Anai

  2. Graduate School of Mathematics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

    Hidenao Iwane & Hirokazu Anai

Authors
  1. Hidenao Iwane
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  2. Hiroyuki Higuchi
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  3. Hirokazu Anai
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Editor information

Editors and Affiliations

  1. Joint Institute for Nuclear Research, Dubna, Moscow Region, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Heinrich-Plett-Straße 40, 34132, Kassel, Germany

    Wolfram Koepf

  3. Technische Universität München, 85748, Garching, Germany

    Ernst W. Mayr

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

    Evgenii V. Vorozhtsov

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Iwane, H., Higuchi, H., Anai, H. (2013). An Effective Implementation of a Special Quantifier Elimination for a Sign Definite Condition by Logical Formula Simplification. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2013. Lecture Notes in Computer Science, vol 8136. Springer, Cham. https://doi.org/10.1007/978-3-319-02297-0_17

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  • DOI: https://doi.org/10.1007/978-3-319-02297-0_17

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02296-3

  • Online ISBN: 978-3-319-02297-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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