Automata, Semigroups and Recognizability of Words on Ordinals
Nicolas Bédon · International Journal of Algebra and Computation · 1998
For a given integer n, we define ωn-semigroups as a generalization of ω-semigroups for languages of words of length less than ωn+1. When they are finite, those algebraic structures define the same sets as those recognized by Choueka automata. These sets are also equivalent to regular expressions in which an unary ω operator standing for the infinite repetition of a language is as free as the Kleene closure operator is. Naturally, the notion of syntactic congruence still works on ωn-semigroups: among all ωn-semigroups recognizing a regular language X, there exists an unique ωn-semigroup of which all others are refinements.