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One-Rule Length-Preserving Rewrite Systems and RationalTransductions

Published online by Cambridge University Press:  21 January 2014

Michel Latteux  and
Yves Roos
Michel Latteux
Affiliation:
Laboratoire d’Informatique Fondamentale de Lille, Université Lille 1, France.. yves.roos@lifl.fr
Yves Roos
Affiliation:
Laboratoire d’Informatique Fondamentale de Lille, Université Lille 1, France.. yves.roos@lifl.fr
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Abstract

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

Keywords

String rewriting - rationality

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Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 48 , Issue 2 , April 2014 , pp. 149 - 171
Copyright
© EDP Sciences 2014

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