no. 2
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
Keywords: string rewriting - rationality 
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     author = {Latteux, Michel and Roos, Yves},
     title = {One-Rule {Length-Preserving} {Rewrite} {Systems} and {Rational} {Transductions}},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {149--171},
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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

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