Complete Variable-Length Codes: An Excursion into Word Edit Operations

Jean Néraud (1, 2)

1 LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes
2 UNIROUEN - Université de Rouen Normandie

Given an alphabet A and a binary relation τ ⊆ A * × A * , a language X ⊆ A * is τ-independent if τ (X) ∩ X = ∅; X is τ-closed if τ (X) ⊆ X. The language X is complete if any word over A is a factor of some concatenation of words in X. Given a family of languages F containing X, X is maximal in F if no other set of F can stricly contain X. A language X ⊆ A * is a variable-length code if any equation among the words of X is necessarily trivial. The study discusses the relationship between maximality and completeness in the case of τ-independent or τ-closed variable-length codes. We focus to the binary relations by which the images of words are computed by deleting, inserting, or substituting some characters.

Mots clés: closed; code; complete; deletion; dependent; detection; distribu- tion; edition; embedding; independent; insertion; Levenshtein; maximal; string; substitution; substring; subword; variable-length; word

Domaines: Informatique et langage [cs.CL]; Mathématique discrète [cs.DM]

Jean Néraud. Complete Variable-Length Codes: An Excursion into Word Edit Operations. LATA 2020, Mar 2020, Milan, Italy. ⟨hal-02389403v2⟩