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

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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.

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Karhumäki, J., & Saarela, A. (2008). An analysis and a reproof of Hmelevskii’s theorem (extended abstract). In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5257 LNCS, pp. 467–478). https://doi.org/10.1007/978-3-540-85780-8_37

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