An analysis and a reproof of Hmelevskii's theorem (extended abstract)

Abstract

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. © 2008 Springer-Verlag Berlin Heidelberg.