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Real Quantifier Elimination in the RegularChains Library

  • Changbo Chen
  • Marc Moreno Maza
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8592)

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.

Keywords

Quantifier elimination cylindrical algebraic decomposition triangular decomposition RegularChains 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Changbo Chen
    • 1
  • Marc Moreno Maza
    • 2
  1. 1.Chongqing Key Laboratory of Automated Reasoning and Cognition, Chongqing Institute of Green and Intelligent TechnologyChinese Academy of SciencesChina
  2. 2.ORCCAUniversity of Western OntarioCanada

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