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Real Quantifier Elimination in the RegularChains Library

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Mathematical Software – ICMS 2014 (ICMS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8592))

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Abstract

Quantifier elimination (QE) over real closed fields has found numerous applications. Cylindrical algebraic decomposition (CAD) is one of the main tools for handling quantifier elimination of nonlinear input formulas. Despite of its worst case doubly exponential complexity, CAD-based quantifier elimination remains interesting for handling general quantified formulas and producing simple quantifier-free formulas.

In this paper, we report on the implementation of a QE procedure, called QuantifierElimination, based on the CAD implementations in the RegularChains library. This command supports both standard quantifier-free formula and extended Tarski formula in the output. The use of the QE procedure is illustrated by solving examples from different applications.

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Author information

Authors and Affiliations

  1. Chongqing Key Laboratory of Automated Reasoning and Cognition, Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, China

    Changbo Chen

  2. ORCCA, University of Western Ontario, Canada

    Marc Moreno Maza

Authors
  1. Changbo Chen
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  2. Marc Moreno Maza
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Editor information

Editors and Affiliations

  1. Department of Mathematics, North Carolina State University, Box 8205, 27695, Raleigh, NC, USA

    Hoon Hong

  2. Courant Institute, Dept. of Computer Science, New York Institute, 251 Mercer Street, 10012, New York, NY, USA

    Chee Yap

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Chen, C., Moreno Maza, M. (2014). Real Quantifier Elimination in the RegularChains Library. In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_44

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  • DOI: https://doi.org/10.1007/978-3-662-44199-2_44

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44198-5

  • Online ISBN: 978-3-662-44199-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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