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

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.

[1]  Arto Salomaa,et al.  Formal languages , 1973, Computer science classics.

[2]  Derrick Wood,et al.  Theory of Computation: A Primer , 1987 .

[3]  Peter Leupold,et al.  Roots and Powers of Regular Languages , 2002, Developments in Language Theory.

[4]  Hugues Calbrix.  Mots ultimement periodiques des langages rationnels de mots infinis , 1996 .

[5]  Thierry Cachat.  The Power of One-Letter Rational Languages , 2001, Developments in Language Theory.

[6]  Derick Wood,et al.  Theory of computation , 1986 .