Reduced Languages as ω-Generators

Abstract

We consider the following decision problem: "Is a rational ω-language generated by a code ?" Since 1994, the codes admit a characterization in terms of infinite words. We derive from this result the definition of a new class of languages, the reduced languages. A code is a reduced language but the converse does not hold. The idea is to "reduce" easy-to-obtain minimal ω-generators in order to obtain codes as ω-generators. Proposition 3. [14] Let L be a language. If L ω is an adherence then χ(L ω) and Stab(L ω) coincide with the greatest ω-generator of L ω .