On generators of rational ω-power languages

Reduced Languages as ω-Generators

“…is not anymore a semigroup. Every ω-generator of L ω is still included in χ(L ω ) and so, when χ(L ω ) is an ω-generator of L ω , it is also the greatest [14].…”

“…One can decide if a rational ω-language admits an ω-generator. If so, a rational ω-generator exists [14]. Various decision problems arise from the set of ω-generators of a given rational ω-language.…”

“…Unfortunately, the set of ω-generators of a rational ω-language does not admit one but a finite number of maximal ω-generators [14]. Even if the greatest ωgenerator exists, the ω-power can be generated by a code without the root of its greatest ω-generator being a code.…”

Rebootable and suffix-closed $\omega $-power languages

“…If L is regular, then Stab(L) is a regular and constructible language. That is, given an automaton which recognizes L, one can construct an automaton recognizing Stab(L) [12]. Hence, one can décide whether L is rebootable.…”

“…oe ) is equal to the monoid Stab^0*). Furthermore, we can construct regular w-generators of R* [12]. Hence we can construct regular rebootable co-generators of R*.…”