One-Rule Length-Preserving Rewrite Systems and Rational Transductions
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 2, pp. 149-171.

We address the problem to know whether the relation induced by a one-rule length-preserving rewrite system is rational. We partially answer to a conjecture of Éric Lilin who conjectured in 1991 that a one-rule length-preserving rewrite system is a rational transduction if and only if the left-hand side u and the right-hand side v of the rule of the system are not quasi-conjugate or are equal, that means if u and v are distinct, there do not exist words x, y and z such that u = xyz and v = zyx. We prove the only if part of this conjecture and identify two non trivial cases where the if part is satisfied.

DOI : 10.1051/ita/2013044
Classification : 68Q45, 68Q42, 68R15
Mots-clés : string rewriting - rationality 
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Latteux, Michel; Roos, Yves. One-Rule Length-Preserving Rewrite Systems and Rational Transductions. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 2, pp. 149-171. doi : 10.1051/ita/2013044. http://archive.numdam.org/articles/10.1051/ita/2013044/

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