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On Non-overlapping Words
Tetsuo MORIYA Itaru KATAOKA
IEICE TRANSACTIONS on Information and Systems
Publication Date: 2011/03/01
Online ISSN: 1745-1361
Print ISSN: 0916-8532
Type of Manuscript: LETTER
Category: Fundamentals of Information Systems
primitive word, non-overlapping word, d-primitive word, context-sensitive, context-free,
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Let Q be the set of all primitive words over a finite alphabet having at least two letters. In this paper, we study the language D(1) of all non-overlapping (d-primitive) words, which is a proper subset of Q. We show that D(1) is a context-sensitive langauage but not a deterministic context-free language. Further it is shown that [D(1)]n is not regular for n ≥ 1.