Efficient Subformula Orders for Real Quantifier Elimination of Non-prenex Formulas

  • Munehiro KobayashiEmail author
  • Hidenao Iwane
  • Takuya Matsuzaki
  • Hirokazu Anai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9582)


In this paper we study speeding up real quantifier elimination (QE) methods for non-prenex formulas. Our basic strategy is to solve non-prenex first-order formulas by performing QE for subformulas constituting the input non-prenex formula. We propose two types of methods (heuristic methods/machine learning based methods) to determine an appropriate ordering of QE computation for the subformulas. Then we empirically examine their effectiveness through experimental results over more than 2,000 non-trivial example problems. Our experiment results suggest machine learning can save much effort spent to design effective heuristics by trials and errors without losing efficiency of QE computation.


Real quantifier elimination Support vector machine Non-prenex formulas 



We thank for the funding from Todai robot project.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Munehiro Kobayashi
    • 1
    Email author
  • Hidenao Iwane
    • 2
    • 3
  • Takuya Matsuzaki
    • 3
    • 4
  • Hirokazu Anai
    • 2
    • 3
    • 5
  1. 1.University of TsukubaTsukubaJapan
  2. 2.Fujitsu Laboratories Ltd.KawasakiJapan
  3. 3.National Institute of InformaticsChiyodaJapan
  4. 4.Nagoya UniversityNagoyaJapan
  5. 5.Kyushu UniversityFukuokaJapan

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