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French translation for "synchronizing word"

mot synchronisant
Example Sentences:
1.For n-state DFAs over a k-letter input alphabet, an algorithm by David Eppstein finds a synchronizing word of length at most 11n3/48 + O(n2), and runs in time complexity O(n3+kn2).
Pour un automate à n
2.This algorithm does not always find the shortest possible synchronizing word for a given automaton; as Eppstein also shows, the problem of finding the shortest synchronizing word is NP-complete.
Cet algorithme ne donne pas toujours le mot synchronisant le plus court pour un automate donné ; Eppstein démontre d'ailleurs que le problème du calcul du plus court mot synchronisant est NP-complet.
3.This algorithm does not always find the shortest possible synchronizing word for a given automaton; as Eppstein also shows, the problem of finding the shortest synchronizing word is NP-complete.
Cet algorithme ne donne pas toujours le mot synchronisant le plus court pour un automate donné ; Eppstein démontre d'ailleurs que le problème du calcul du plus court mot synchronisant est NP-complet.
4.That is, if an ensemble of copies of the DFA are each started in different states, and all of the copies process the synchronizing word at the same speed, they will all end up reaching the same state as each other, at the same time as each other.
En d'autres termes, si un ensemble de copies de l'automate démarre, simultanément chacune en un état différent, elles se trouvent toutes après la lecture du mot synchronisant en même temps dans le même état.
5.However, for a special class of automata in which all state transitions preserve the cyclic order of the states, he describes a different algorithm with time O(kn2) that always finds the shortest synchronizing word, proves that these automata always have a synchronizing word of length at most (n − 1)2 (the bound given in Černý's conjecture), and exhibits examples of automata with this special form whose shortest synchronizing word has length exactly (n − 1)2.
Il donne toutefois une classe d'automates pour lesquels un algorithme en temps O ( k n 2 )
6.However, for a special class of automata in which all state transitions preserve the cyclic order of the states, he describes a different algorithm with time O(kn2) that always finds the shortest synchronizing word, proves that these automata always have a synchronizing word of length at most (n − 1)2 (the bound given in Černý's conjecture), and exhibits examples of automata with this special form whose shortest synchronizing word has length exactly (n − 1)2.
Il donne toutefois une classe d'automates pour lesquels un algorithme en temps O ( k n 2 )
7.However, for a special class of automata in which all state transitions preserve the cyclic order of the states, he describes a different algorithm with time O(kn2) that always finds the shortest synchronizing word, proves that these automata always have a synchronizing word of length at most (n − 1)2 (the bound given in Černý's conjecture), and exhibits examples of automata with this special form whose shortest synchronizing word has length exactly (n − 1)2.
Il donne toutefois une classe d'automates pour lesquels un algorithme en temps O ( k n 2 )
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