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Quantifier Elimination over Finite Fields Using Gr\"obner Bases

By Sicun Gao, André Platzer and Edmund M. Clarke

Abstract

We give an algebraic quantifier elimination algorithm for the first-order theory over any given finite field using Gr\"obner basis methods. The algorithm relies on the strong Nullstellensatz and properties of elimination ideals over finite fields. We analyze the theoretical complexity of the algorithm and show its application in the formal analysis of a biological controller model.Comment: A shorter version is to appear in International Conference on Algebraic Informatics 201

Topics: Computer Science - Symbolic Computation, Computer Science - Logic in Computer Science
Year: 2011
DOI identifier: 10.1007/978-3-642-21493-6_9
OAI identifier: oai:arXiv.org:1104.0746
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