On the Complexity of Hmelevskii’s Theorem and Satisfiability of Three Unknown Equations

  • Aleksi Saarela
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5583)

Abstract

We analyze Hmelevskii’s theorem, which states that the general solutions of constant-free equations on three unknowns are expressible by a finite collection of formulas of word and numerical parameters. We prove that the size of the finite representation is bounded by an exponential function on the size of the equation. We also prove that the shortest nontrivial solution of the equation, if it exists, is exponential, and that its existence can be solved in nondeterministic polynomial time.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Aleksi Saarela
    • 1
  1. 1.Department of Mathematics and Turku Centre for Computer Science TUCSUniversity of TurkuTurkuFinland

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