Context-free and stationary languagest†

A stationary word of a OL system G=(X,P,w) is a word that generates itself after a positive number of direct derivations. The stationary set of G is the set of stationary words of G and the stationary language of G is the set of the stationary words generated by w. The stationary set of G is a submonoid of X * containing the adult set of G. A language not containing the empty word is context-free if and only if it is the stationary language of a propagating system. Every TOL language is the image under a coding of the stationary language of a TOL system.