Locally complete sets and finite decomposable codes

Néraud, Jean; Selmi, Carla

doi:10.1016/s0304-3975(00)00440-0

Cited by 5 publications

(2 citation statements)

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“…Following this approach, in [36] the authors proved that we can decide whether a free submonoid C * is maximal when C is a rational maximal prefix code. Furthermore, a polynomial time algorithm has been given for deciding the maximality of C * when C is a finite maximal prefix code in [11] and when C is a finite maximal code in [28]. The latter algorithm is a consequence of results given in the same paper [28] on locally complete sets.…”

Section: Composition and Substitutionmentioning

confidence: 99%

“…Furthermore, a polynomial time algorithm has been given for deciding the maximality of C * when C is a finite maximal prefix code in [11] and when C is a finite maximal code in [28]. The latter algorithm is a consequence of results given in the same paper [28] on locally complete sets. Informally, the notion of a locally complete set arises in connection with the attempt to define maximality and completeness of a code with respect to a set which has more constraints than the free monoid (as also done in [20,34] with different viewpoints).…”

Section: Composition and Substitutionmentioning

confidence: 99%

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On a complete set of operations for factorizing codes

Felice

2005

RAIRO-Theor. Inf. Appl.

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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. Mathematics Subject Classification. 94A45, 68Q45, 20K01.Article published by EDP Sciences and available at http://www.edpsciences.org/ita or http://dx.

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Section: Composition and Substitutionmentioning

confidence: 99%