Sturmian and Infinitely Desubstitutable Words Accepted by an $$\omega $$-Automaton

Hopcroft’s automaton minimization algorithm and Sturmian words

An algorithm for the minimization of deterministic finite state automata that runs in time O(n log n) on automata with n states was given by Hopcroft (1971). It is, up to now, the most efficient algorithm known in the general case. We address here the problem of showing that the running time O(n log n) for Hopcroft algorithms is tight. This algorithm has a degree of freedom because, in each ste...

Return words in Sturmian and episturmian words

Considering each occurrence of a word w in a recurrent infinite word, we define the set of return words of w to be the set of all distinct words beginning with an occurrence of w and ending exactly just before the next occurrence of w in the infinite word. We give a simpler proof of the recent result (of the second author) that an infinite word is Sturmian if and only if each of its factors has...

Sturmian Words: Dynamical Systems and Derivated Words

Sturmian Words, Lyndon Words and Trees

We prove some new combinatorial properties of the set PER of all words w having two periods p and q which are coprimes and such that w = p + q 2 [4,3]. We show that aPERb U {a, b} = St n Lynd, where St is the set of the finite factors of all infinite Sturmian words and Lynd is the set of the Lyndon words on the alphabet {a, b}. It is also shown that aPERb U {a, b} = CP, where CP is the set of C...

A Characterization of Sturmian Words by Return Words

1 R esum e: Nous pr esentons une nouvelle caract erisation des mots de Sturm bas ee sur les mots de retour. Si l'on consid ere chaque occurrence d'un mot w dans un mot innni r ecurrent, on d eenit l'ensemble des mots de retour de w comme l'ensemble de tous les mots distincts commenn cant par une occurrence de w et nissant exactement avant l'occurrence suivante de w. Le r esultat principal montr...