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 : https://doi.org/10.1051/ita/2013044
Classification : 68Q45,  68Q42,  68R15
Mots clés : string rewriting - rationality
@article{ITA_2014__48_2_149_0,
     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},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {2},
     year = {2014},
     doi = {10.1051/ita/2013044},
     mrnumber = {3302482},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ita/2013044/}
}
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://www.numdam.org/articles/10.1051/ita/2013044/

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