An analysis and a reproof of Hmelevskii's theorem
J Karhumäki, A Saarela - International Conference on Developments in …, 2008 - Springer
International Conference on Developments in Language Theory, 2008•Springer
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.
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.
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.
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