An Analysis and a Reproof of Hmelevskii’s Theorem

(Extended Abstract)
  • Juhani Karhumäki
  • Aleksi Saarela
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5257)


We analyze and reprove the famous theorem of Hmelevskii, which states that the general solutions of constant-free equations on three unknowns are finitely parameterizable, that is expressible by a finite collection of formulas of word and numerical parameters. The proof is written, and simplified, by using modern tools of combinatorics on words. As a new aspect the size of the finite representation is estimated; it is bounded by a double exponential function on the size of the equation.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

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

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