The finite power property for context-free languages

Abstract

A language L is said to have the finite power property if there exists some positive integer n such that L* = ({A} u ~5)“. The problem of determining for which classes of languages the finite power property is decidable was first posed by J.A. Brzozowski in 1966. Simon [4j has developed a decision procedure for the class of regular languages. Our major result is to prove that this problem is undecidable for the class of context-free languages. As a preliminary, we will first establish the Unsolvability of the conceptually easier probfem of testing if L = L2 for context-free Pianguages.