The Degree of a Finite Set of Words - Models and Algorithms Accéder directement au contenu
Communication Dans Un Congrès Année : 2020

The Degree of a Finite Set of Words

Résumé

We generalize the notions of the degree and composition from uniquely decipherable codes to arbitrary finite sets of words. We prove that if X = Y∘Z is a composition of finite sets of words with Y complete, then d(X) = d(Y) ⋅ d(Z), where d(T) is the degree of T. We also show that a finite set is synchronizing if and only if its degree equals one. This is done by considering, for an arbitrary finite set X of words, the transition monoid of an automaton recognizing X^* with multiplicities. We prove a number of results for such monoids, which generalize corresponding results for unambiguous monoids of relations.
Fichier principal
Vignette du fichier
LIPIcs.FSTTCS.2020.54.pdf (551.17 Ko) Télécharger le fichier
Origine Fichiers éditeurs autorisés sur une archive ouverte

Dates et versions

hal-04491375 , version 1 (06-03-2024)

Licence

Identifiants

Citer

Dominique Perrin, Andrew Ryzhikov. The Degree of a Finite Set of Words. FSTTCS 2020, Dec 2020, Goa (online), India. pp.54:1-54:16, ⟨10.4230/LIPICS.FSTTCS.2020.54⟩. ⟨hal-04491375⟩
14 Consultations
3 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More