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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
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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References

J. Berstel, Transductions and Context-Free Languages. Teubner Verlag (1979).
M. Clerbout and Y. Roos, Semi-commutations and algebraic languages, in STACS 90, in vol. 415, edited by Christian Choffrut and Thomas Lengauer. Lect. Notes Comput. Sci. Springer Berlin/Heidelberg (1990) 82–94.
N. Dershowitz, Open. closed. open, in vol. 3467 of Lect. Notes Comput. Sci. RTA, edited by J. Giesl. Springer (2005) 376–393.
S. Eilenberg and B. Tilson, Automata, languages and machines, vol. B, Pure Appl. Math. Academic Press, New York, San Francisco, London (1976).
A. Geser, Termination of string rewriting rules that have one pair of overlaps, in vol. 2706, Lect. Notes Comput. Sci. RTA, edited by R. Nieuwenhuis. Springer (2003) 410–423.
Geser, A., Hofbauer, D., and Waldmann, J., Match-bounded string rewriting systems. Appl. Algebra Eng. Commun. Comput. 15 (2004) 149–171. Google Scholar
W. Kurth, Termination und Konfluenz von Semi–Thue–Systemen mit nur einer Regel. Ph.D. thesis, Technische Universitt Clausthal (1990).
M. Latteux and Y. Roos, The image of a word by a one-rule semi-Thue system is not always context-free (2011). http://www.lifl.fr/ỹroos/al/one-rule-context-free.pdf.
É. Lilin, Une généralisation des semi-commutations. Technical Report IT-210, Laboratoire d’Informatique Fondamentale de Lille, Université de Lille 1, France (1991). In french.
Métivier, Y., Calcul de longueurs de chaînes de reé´criture dans le monoïde libre. Theor. Comput. Sci. 35 (1985) 71–87. Google Scholar
R. Milner, The spectra of words, in vol. 3838 of Processes, Terms and Cycles: Steps on the Road to Infinity, edited by A. Middeldorp, V. van Oostrom, F. van Raamsdonk and R. de Vrijer. Lect. Notes Comput. Sci. Springer Berlin/Heidelberg (2005) 1–5.
Ravikumar, B., Peg-solitaire, string rewriting systems and finite automata. Theor. Comput. Sci. 321 (2004) 383–394. Google Scholar
J. Sakarovitch, Elements of Automata Theory. Cambridge University Press, New York, USA (2009).
J. Sakarovitch and I. Simon, Subwords. In Combinatorics on words. Cambridge Mathematical Library. Cambridge University Press (1997) 105–142.
Terlutte, A. and Simplot, D., Iteration of rational transductions. RAIRO: ITA 34 (2000) 99–130. Google Scholar
C. Wrathall, Confluence of one-rule thue systems, Word Equations and Related Topics, in vol. 572 of Lect. Notes Comput. Sci., edited by K. Schulz. Springer Berlin/Heidelberg (1992) 237–246.