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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.
@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://geodesic.mathdoc.fr/articles/10.1051/ita/2013044/}
}
TY - JOUR AU - Latteux, Michel AU - Roos, Yves TI - One-Rule Length-Preserving Rewrite Systems and Rational Transductions JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2014 SP - 149 EP - 171 VL - 48 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ita/2013044/ DO - 10.1051/ita/2013044 LA - en ID - ITA_2014__48_2_149_0 ER -
%0 Journal Article %A Latteux, Michel %A Roos, Yves %T One-Rule Length-Preserving Rewrite Systems and Rational Transductions %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2014 %P 149-171 %V 48 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ita/2013044/ %R 10.1051/ita/2013044 %G en %F ITA_2014__48_2_149_0
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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