Local quantifier elimination

Authors:
Andreas Dolzmann;Volker Weispfenning
Affiliations:
Department of Mathematics and Computer Science, University of Passau, Germany;Department of Mathematics and Computer Science, University of Passau, Germany
Venue:
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Year:
2000

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Abstract

We introduce local quantifier elimination as a new variant of real quantifier elimination. Given a first-order formula and a real point we compute a quantifier-free formula which is not only for the given point equivalent to the input formula but also for all points in a semi-algebraic set containing the specified point. The description of this semi-algebraic set is explicitly computed in the form of a conjunction of atomic formulas. Local quantifier elimination is in its application area superior to both regular and generic quantifier elimination due to faster running times and shorter results.