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TitleVariant quantifier elimination
Author(s) Hoon Hong, Mohab Safey
TypeArticle in Journal
AbstractWe describe an algorithm (VQE) for a variant of the real quantifier elimination problem (QE). The variant problem requires the input to satisfy a certain extra condition, and allows the output to be 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.
KeywordsQuantifier elimination, Computational real algebraic geometry, Stability analysis
URL http://www.sciencedirect.com/science/article/pii/S0747717111002057
JournalJournal of Symbolic Computation
Pages883 - 901
NoteInternational Symposium on Symbolic and Algebraic Computation (ISSAC 2009)
Translation No
Refereed No