Abstract
Although it is decidable whether or not a word equation is satisfiable, due to Makanin’s results, the structure of all solutions in general is difficult to describe. In particular, it was proved by Hmelevskii that the solutions of xyz=zvx cannot be finitely parametrized, contrary to the case of equations in three unknowns. In this paper we give a short, elementary proof of Hmelevkii’s result. We also give a simple, necessary, non-sufficient condition for an equation to be non-parametrizable.
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Petre, E. (2004). An Elementary Proof for the Non-parametrizability of the Equation xyz=zvx . In: Fiala, J., Koubek, V., Kratochvíl, J. (eds) Mathematical Foundations of Computer Science 2004. MFCS 2004. Lecture Notes in Computer Science, vol 3153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28629-5_63
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DOI: https://doi.org/10.1007/978-3-540-28629-5_63
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