Roots and powers of regular languages

Authors:
Sándor Horváth;Peter Leupold;Gerhard Lischke
Affiliations:
Department of Computer Science, Institute I of Mathematics, Eötvös Loránd University, Budapest, Hungary;Research Group in Mathematical Linguistics, University Rovira i Virgili, Tarragona, Spain;Institute of Informatics, Faculty of Mathematics and Informatics, Friedrich Schiller University Jena, Jena, Germany
Venue:
DLT'02 Proceedings of the 6th international conference on Developments in language theory
Year:
2002

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Abstract

For a set H of natural numbers, the H-power of a language L is the set of all words pk where p ∈ L and k ∈ H. The root of L is the set of all primitive words p such that pn belongs to L for some n ≥ 1. There is a strong connection between the root and the powers of a regular language L namely, the H-power of L for an arbitrary finite set H with 0, 1, 2 ∉ H is regular if and only if the root of L is finite. If the root is infinite then the H-power for most regular sets H is context-sensitive but not context-free. The stated property is decidable.