On a complete set of operations for factorizing codes

Felice, Clelia De

doi:10.1051/ita:2005040

Felice, Clelia De

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 1, pp. 29-52.

Résumé

It is known that the class of factorizing codes, i.e., codes satisfying the factorization conjecture formulated by Schützenberger, is closed under two operations: the classical composition of codes and substitution of codes. A natural question which arises is whether a finite set $𝒪$ of operations exists such that each factorizing code can be obtained by using the operations in $𝒪$ and starting with prefix or suffix codes. $𝒪$ is named here a complete set of operations (for factorizing codes). We show that composition and substitution are not enough in order to obtain a complete set. Indeed, we exhibit a factorizing code over a two-letter alphabet $A = {a, b}$ , precisely a $3 -$ code, which cannot be obtained by decomposition or substitution.

MR Zbl

DOI : 10.1051/ita:2005040

Classification : 94A45, 68Q45, 20K01
Mots clés : variable length codes, formal languages, factorizations of cyclic groups

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Felice, Clelia De. On a complete set of operations for factorizing codes. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 1, pp. 29-52. doi : 10.1051/ita:2005040. http://archive.numdam.org/articles/10.1051/ita:2005040/

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