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One-Rule Length-Preserving Rewrite Systems and Rational Transductions

Michel Latteux, Yves Roos (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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...

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