Une note sur la propriété de préfixe

Latteux, Michel

doi:10.1007/bf01768478

Cited by 4 publications

(3 citation statements)

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“…Book formulated the "prefix property" in order to allow languages to "approximate" infinite sequences, and showed that for certain classes of languages, if a language in the class has the prefix property, then it is regular. A follow-up by Latteux [14] gives a necessary and sufficient condition for a prefix language to be regular. Languages whose complement is a prefix language, called "coprefix languages", have also been studied; see Berstel [4] for a survey of results on infinite words whose coprefix language is context-free.…”

Section: Related Workmentioning

confidence: 99%

On Infinite Words Determined by Indexed Languages

Smith

2014

Lecture Notes in Computer Science

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We characterize the infinite words determined by indexed languages. An infinite language L determines an infinite word α if every string in L is a prefix of α. If L is regular or context-free, it is known that α must be ultimately periodic. We show that if L is an indexed language, then α is a morphic word, i.e., α can be generated by iterating a morphism under a coding. Since the other direction, that every morphic word is determined by some indexed language, also holds, this implies that the infinite words determined by indexed languages are exactly the morphic words. To obtain this result, we prove a new pumping lemma for the indexed languages, which may be of independent interest.

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Section: Related Workmentioning

confidence: 99%

On Infinite Words Determined by Indexed Languages

Smith

2014

Lecture Notes in Computer Science

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“…Démonstration ; L'équivalence entre (i), (ii) et (iii) a été établie dans [5]. D'autre part, il est clair que (ii) implique (iv) et (v).…”

Section: Préliminairesunclassified

“…En fait, dès que ^£ est clos par intersection avec les langages rationnels et par homomorphisme, cette propriété est équivalente à : tout langage de S£ défini sur un alphabet d'une seule lettre est rationnel (cf. [5] Nous allons considérer, dans ce papier, une propriété un peu plus faible en nous restreignant aux langages qui ont la propriété de préfixe et qui vérifient L = Init (L) = { x/3 y, xy e L }. Chacun de ces langages est l'ensemble des facteurs gauches d'un mot infini (cf.…”

Section: Introductionunclassified