Séminaire du 6 avril 2009.
10h30: Variant Real Quantifier Elimination: Algorithm, Implementation, Complexity and Application. Mohab Safey El Din, LIP6 et Projet SALSA de l'Inria Paris-Rocquencourt
We study a variant of real quantifier elimination problem
(QE). The variant problem requires the input to satisfy a certain
extra condition, and allows the ouput to be almost
equivalent to the input. In a sense, we are strengthening the
pre-condition and weakening the post-condition of the standard QE
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 ouput formula is almost equivalent to the input formula.
We present an algorithm (VQE) , that exploits the strengthened
pre-condition and the weakened post-condition.
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 VQE 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 1
day. Joint work with Hoon Hong, North Carolina State University.
Last modified: Mon Mar 30 17:40:36 CEST 2009