Generalization of the Ginsburg-Rice Schützenberger fixed-point theorem for context-sensitive and recursive-enumerable languages

Abstract

The paper generalizes the Ginsburg-Rice Schützenberger ALGOL-like fixed-point theorem showing that every λ-free context-sensitive (recursive-enumerable) language is a component of the least fixed-point of a system of equations in the form X = F( X), where X = ( X 1,…, X t ), F = ( F 1,…, F t ), t⩾1 and for all i, 1⩽ i⩽ t, F i are regular expre ssions over the alphabet of operations: {union, concatenation, Kleene+ (∗) closure, nonerasing finite substitution (arbitrary finite substitution), intersection}. Fixed-point characterization theorems for these families of languages are also presented.