Finiteness and Regularity in Semigroups and Formal Languages

On Bounded Rational Trace Languages

“…The first one shows that the notion is meaningful since it is in a sense intrinsic. Its proof easily follows from that one of [10], Lemma 3.2.3.…”

From Bi-ideals to Periodicity

“…Our terminology is more or less standard (cf. [10]) so that a specialist reader may wish to consult this section only if need arise. Let A be a finite non-empty set and A * the free monoid generated by A.…”

“…(see, e.g., [10]) Let x ∈ A ω be an ultimately periodic word. If x is recurrent, then x is periodic.…”

“…This hierarchy comes from combinatorics on words, where these classes are being investigated intensively (cf. [2,8,9,10]). Bi-ideal sequences have been considered, with different names, by several authors in algebra and combinatorics [1,3,7,13,17].…”

Open Problems on Partial Words

“…Several books have appeared quite recently that emphasize connections of combinatorics on words to several research areas. We mention the book of Allouche and Shallit where the emphasis is on automata theory [2], the book of Crochemore and Rytter where the emphasis is on string algorithms [52], the book of Gusfield where the emphasis is on algorithms related to biology [72], the book of de Luca and Varrichio where the emphasis is on algebra [55], and finally the book of Blanchet-Sadri where the emphasis is on partial words [10].…”