Quantifier Elimination over Finite Fields Using Gröbner Bases

  • Sicun Gao
  • André Platzer
  • Edmund M. Clarke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6742)


We give an algebraic quantifier elimination algorithm for the first-order theory over any given finite field using Gröbner 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.


Finite Field Decision Procedure Free Variable Atomic Formula Safety Property 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Sicun Gao
    • 1
  • André Platzer
    • 1
  • Edmund M. Clarke
    • 1
  1. 1.Carnegie Mellon UniversityPittsburghUSA

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