Context-Free Languages

Abstract

The first section of this chapter contains the definitions of context-free or algebraic languages by means of context-free grammars and of systems of algebraic equations. In the second section, we recall without proof several constructions and closure properties of context-free languages. This section contains also the iteration lemmas for context-free languages. The third section gives a description of the various families of Dyck languages. They have two definitions, as classes of certain congruences, and as languages generated by some context-free grammars. The section ends with a proof of the Chomsky-Schützenberger Theorem. Two other languages, the Lukasiewicz language and the language of completely parenthesized arithmetic expressions, are studied in the last section.