Compatibility relations on codes and free monoids
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 3, pp. 539-552.

A compatibility relation on letters induces a reflexive and symmetric relation on words of equal length. We consider these word relations with respect to the theory of variable length codes and free monoids. We define an $\left(R,S\right)$-code and an $\left(R,S\right)$-free monoid for arbitrary word relations $R$ and $S$. Modified Sardinas-Patterson algorithm is presented for testing whether finite sets of words are $\left(R,S\right)$-codes. Coding capabilities of relational codes are measured algorithmically by finding minimal and maximal relations. We generalize the stability criterion of Schützenberger and Tilson’s closure result for $\left(R,S\right)$-free monoids. The $\left(R,S\right)$-free hull of a set of words is introduced and we show how it can be computed. We prove a defect theorem for $\left(R,S\right)$-free hulls. In addition, a defect theorem of partial words is proved as a corollary.

DOI : https://doi.org/10.1051/ita:2008016
Classification : 68R15
Mots clés : compatibility relation, free monoid, stability, defect theorem, partial word
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author = {K\"arki, Tomi},
title = {Compatibility relations on codes and free monoids},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {539--552},
publisher = {EDP-Sciences},
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doi = {10.1051/ita:2008016},
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language = {en},
url = {http://www.numdam.org/articles/10.1051/ita:2008016/}
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Kärki, Tomi. Compatibility relations on codes and free monoids. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 3, pp. 539-552. doi : 10.1051/ita:2008016. http://www.numdam.org/articles/10.1051/ita:2008016/

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