Compatibility relations on codes and free monoids

Kärki, Tomi

doi:10.1051/ita:2008016

Kärki, Tomi

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 3, pp. 539-552.

Résumé

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 $(R, S)$ -code and an $(R, S)$ -free monoid for arbitrary word relations $R$ and $S$ . Modified Sardinas-Patterson algorithm is presented for testing whether finite sets of words are $(R, S)$ -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 $(R, S)$ -free monoids. The $(R, S)$ -free hull of a set of words is introduced and we show how it can be computed. We prove a defect theorem for $(R, S)$ -free hulls. In addition, a defect theorem of partial words is proved as a corollary.

MR Zbl

DOI : 10.1051/ita:2008016

Classification : 68R15
Mots clés : compatibility relation, free monoid, stability, defect theorem, partial word

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     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},
     volume = {42},
     number = {3},
     year = {2008},
     doi = {10.1051/ita:2008016},
     mrnumber = {2434034},
     zbl = {1149.68069},
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     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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