Langages algébriques de mots biinfinis. (Algebraic languages of biinfinite words) (Q1178712)

A rational language of bi-infinite strings is a finite union of languages of the form \(^ \omega ABC^ \omega\), where \(A\), \(B\), \(C\) are usual regular languages. The aim of the paper is to define algebraic languages of bi-infinite strings. Three different approaches are used, leading to three different families, \({\mathcal C}_ 0\), \({\mathcal C}_ 1\), \({\mathcal C}_ 2\) for which the strict inclusions \({\mathcal C}_ 2\subset{\mathcal C}_ 1\subset{\mathcal C}_ 0\) hold. \({\mathcal C}_ 0\) is the infinite rational closure of algebraic (context-free, in the usual terminology) languages of finite strings, \({\mathcal C}_ 1\) is the family of languages of the form \(L^ \omega(G,v)\), of infinite strings generated by a context-free grammar \(G\) with the axiom \(v\), and \({\mathcal C}_ 2\) is the family of languages of infinite strings which are the adherence of context-free languages of finite strings.