Quantifier Elimination over Finite Fields Using Gröbner Bases

Details Quantifier Elimination over Finite Fields Using Gröbner Bases Quantifier Elimination over Finite Fields Using Gröbner Bases

2011-04-05

arxiv.org/abs/1104.0746v1

Computer Science

Symbolic Computation

A shorter version is to appear in International Conference on Algebraic Informatics 2011

Scientific paper

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.

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