Quantifier Elimination over Finite Fields Using Gr\"obner Bases
  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. 
Sicun Gao, Andr\'e Platzer and Edmund M. Clarke
cs.SC cs.LO