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d-Primitive Words and D(1)-Concatenated Words
Itaru KATAOKA Tetsuo MORIYA
IEICE TRANSACTIONS on Information and Systems
Publication Date: 2009/08/01
Online ISSN: 1745-1361
Print ISSN: 0916-8532
Type of Manuscript: LETTER
Category: Automata and Formal Language Theory
primitive word, d-primitive word, regular component,
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In this paper, we study d-primitive words and D(1)-concatenated words. First we show that neither D(1), the set of all d-primitive words, nor D(1)D(1), the set of all D(1)-concatenated words, is regular. Next we show that for u, v, w ∈Σ+ with |u|=|w|, uvw ∈ D(1) if and only if uv+w ⊆ D(1). It is also shown that every d-primitive word, with the length of two or more, is D(1)-concatenated.