Details:
Title  Variant quantifier elimination  Author(s)  Hoon Hong, Mohab Safey  Type  Article in Journal  Abstract  We 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 widelyused 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.  Keywords  Quantifier elimination, Computational real algebraic geometry, Stability analysis  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717111002057 
Language  English  Journal  Journal of Symbolic Computation  Volume  47  Number  7  Pages  883  901  Year  2012  Note  International Symposium on Symbolic and Algebraic Computation (ISSAC 2009)  Edition  0  Translation 
No  Refereed 
No 
