Context-freeness of the power of context-free languages is undecidable

Authors:
Henning Bordihn
Affiliations:
Institut für Informatik, Universität Potsdam, August-Bebel-Straße 89, Haus 4, D-14482 Potsdam, Germany
Venue:
Theoretical Computer Science
Year:
2004

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Abstract

The power of a language L is the set of all powers of the words in L. In this paper, the following decision problem is investigated. Given a context-free language L, is the power of L context-free? We show that this problem is decidable for languages over unary alphabets, but it is undecidable whenever languages over alphabets with at least two letters are considered.