Generators

Abstract

The first section contains examples of generators of the cone Alg of context-free languages. The Dyck languages over at least two pairs of parentheses and the language E of completely parenthesized arithmetic expressions are shown to be generators. Sections 2 and 3 are concerned with S. Greibach’s Syntactic Lemma and its applications. In particular, we prove that in a substitution closed principal full AFL, the nongenerators form a substitution closed full AFL. Next the Syntactic Lemma is used to exhibit infinite ascending chains of cones, and thus nonprincipal cones of context-free languages. In Section 4, we study the family of languages recognized by one counter pushdown automata and we prove this family to be the full AFL generated by D ^′₁ *. The last section deals with the family of quasi-rational or nonexpansive languages. Several characterizations of this family are given.