Analysing All Polynomial Equations in \({\mathbb Z_{2^w}}\)

  • Helmut Seidl
  • Andrea Flexeder
  • Michael Petter
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5079)


In this paper, we present methods for checking and inferring all valid polynomial relations in \({\mathbb Z_{2^w}}\). In contrast to the infinite field ℚ, \({\mathbb Z_{2^w}}\) is finite and hence allows for finitely many polynomial functions only. In this paper we show, that checking the validity of a polynomial invariant over \({\mathbb Z_{2^w}}\) is, though decidable, only PSPACE-complete. Apart from the impracticable algorithm for the theoretical upper bound, we present a feasible algorithm for verifying polynomial invariants over \({\mathbb Z_{2^w}}\) which runs in polynomial time if the number of program variables is bounded by a constant. In this case, we also obtain a polynomial-time algorithm for inferring all polynomial relations. In general, our approach provides us with a feasible algorithm to infer all polynomial invariants up to a low degree.


Total Degree Constraint System Program Variable Quotient Ring Polynomial Invariant 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Helmut Seidl
    • 1
  • Andrea Flexeder
    • 1
  • Michael Petter
    • 1
  1. 1.Technische Universität MünchenGarchingGermany

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