Fair derivations in context-free grammars

Abstract

This paper connects between notions of pure formal language theory and nondeterministic programming. The notion of a fair derivation in a context-free grammar is defined, whereby for every variable appearing infinitely often in sentential forms of an infinite derivation, each of its rules is used infinitely often. A context-free language is fairly generated if it has a grammar all of whose fair derivations are finite. It is proved that a context-free grammar is fairly terminating iff it is non-expansive.