Le problème de la synchronisation et la conjecture de Cerný - Archive ouverte HAL
Chapitre D'ouvrage Année : 1981

Le problème de la synchronisation et la conjecture de Cerný

Résumé

We give a survey on the following problem (known as the synchronization problem). Let A = (Q, X) be a finite automaton. Every word m in X* defines a function from Q into Q; the rank of m in A is the integer Card {qm ¦ q in Q }. A word of rank 1 maps all the states onto a single state and is called a synchronizing word (if such a word exists, the automaton itself is called synchronizing). Let A an automaton with n states. Cerný has conjectured that if A is synchronizing, then there exists a synchronizing word of length ≤ (n-1)^2. A generalization of this conjecture states that if there exists a word of rank ≤ k in A, then there exists such a word of length ≤ (n-k)^2.

Mots clés

Fichier principal
Vignette du fichier
CernyCNR.pdf (161.31 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00340776 , version 1 (22-11-2008)

Identifiants

  • HAL Id : hal-00340776 , version 1

Citer

Jean-Eric Pin. Le problème de la synchronisation et la conjecture de Cerný. A. De Luca. Non-commutative structures in algebra and geometric combinatorics vol. 109, CNR (Consiglio nazionale delle ricerche, Italy), pp.37-48, 1981, Quaderni de la Ricerca Scientifica. ⟨hal-00340776⟩
242 Consultations
213 Téléchargements

Partager

More