Finite generation of ambiguity in context-free languages

Abstract

This paper presents a pair of sufficient conditions, within an algebraic model of the generation of context-free languages, so that the intersection of two context-free languages is finitely partitioned by common sublanguages. When such a context-free algebraic system satisfies this pair of sufficient conditions, the ambiguity in deriving strings of symbols is shown to be finitely generated. These conditions cannot be necessary, because these problems are equivalent to the language equivalence problem for context-free grammars, which is undecidable.