Real Quantifier Elimination in the RegularChains Library
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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.
KeywordsQuantifier elimination cylindrical algebraic decomposition triangular decomposition RegularChains
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- 1.Basu, S., Pollack, R., Roy, M.-F.: Algorithms in real algebraic geometry. Algorithms and Computations in Mathematics, vol. 10. Springer (2006)Google Scholar
- 2.Bradford, R., Chen, C., Davenport, J.H., England, M., Moreno Maza, M., Wilson, D.: Truth table invariant cylindrical algebraic decomposition by regular chains (submitted, 2014), Preprint: http://opus.bath.ac.uk/38344/
- 3.Brown, C.W.: Solution Formula Construction for Truth Invariant CAD’s. PhD thesis, University of Delaware (1999)Google Scholar
- 4.Chen, C., Moreno Maza, M.: Quantifier elimination by cylindrical algebraic decomposition based on regular chains (Accepted for ISSAC 2014) (2014)Google Scholar
- 5.Chen, C., Moreno Maza, M.: An incremental algorithm for computing cylindrical algebraic decompositions. In: Proc. ASCM 2012 (October 2012)Google Scholar
- 6.Chen, C., Moreno Maza, M., Xia, B., Yang, L.: Computing cylindrical algebraic decomposition via triangular decomposition. In: ISSAC 2009, pp. 95–102 (2009)Google Scholar
- 7.Collins, G.E.: Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In: Brakhage, H. (ed.) GI-Fachtagung 1975. LNCS, vol. 33, pp. 515–532. Springer, Heidelberg (1975)Google Scholar
- 9.Hong, H.: Simple solution formula construction in cylindrical algebraic decomposition based quantifier elimination. In: ISSAC, pp. 177–188 (1992)Google Scholar
- 10.Sturm, T., Tiwari, A.: Verification and synthesis using real quantifier elimination. In: ISSAC, pp. 329–336 (2011)Google Scholar
- 11.Tarski, A.: A decision method for elementary algebra and geometry. University of California Press (1951)Google Scholar