Variant Quantifier Elimination - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of Symbolic Computation Year : 2012

Variant Quantifier Elimination

Hoon Hong
  • Function : Author
  • PersonId : 935617
Mohab Safey El Din

Abstract

We describe an algorithm (VQE)\ for a \emph{variant} of the real quantifier elimination problem (QE). The variant problem requires the input to satisfy a certain \emph{extra condition}, and allows the output to be \emph{almost} equivalent to the input. The motivation/rationale for studying such a variant QE problem is that many quantified formulas arising in applications do satisfy the extra conditions. Furthermore, in most applications, it is sufficient that the output formula is almost equivalent to the input formula. The main idea underlying the algorithm is to substitute the repeated projection step of CAD by a single projection without carrying out a parametric existential decision over the reals. We find that the algorithm can tackle important and challenging problems, such as numerical stability analysis of the widely-used MacCormack's scheme. The problem has been practically out of reach for standard QE algorithms in spite of many attempts to tackle it. However the current implementation of VQE can solve it in about 12 hours. This paper extends the results reported at the conference ISSAC~2009.
Fichier principal
Vignette du fichier
vqe_jsc_final.pdf (525.73 Ko) Télécharger le fichier
Origin Publisher files allowed on an open archive
Loading...

Dates and versions

hal-00778365 , version 1 (19-01-2013)

Identifiers

Cite

Hoon Hong, Mohab Safey El Din. Variant Quantifier Elimination. Journal of Symbolic Computation, 2012, International Symposium on Symbolic and Algebraic Computation (ISSAC 2009), 47 (7), pp.883-901. ⟨10.1016/j.jsc.2011.05.014⟩. ⟨hal-00778365⟩
177 View
204 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More