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.
Supported by the Academy of Finland under grant 8121419.
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Karhumäki, J., Saarela, A. (2008). An Analysis and a Reproof of Hmelevskii’s Theorem. In: Ito, M., Toyama, M. (eds) Developments in Language Theory. DLT 2008. Lecture Notes in Computer Science, vol 5257. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85780-8_37
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DOI: https://doi.org/10.1007/978-3-540-85780-8_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85779-2
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