d-Primitive Words and D(1)-Concatenated Words
Summary :
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.
- Publication
- IEICE TRANSACTIONS on Information Vol.E92-D No.8 pp.1577-1579
- Publication Date
- 2009/08/01
- Publicized
- Online ISSN
- 1745-1361
- DOI
- 10.1587/transinf.E92.D.1577
- Type of Manuscript
- LETTER
- Category
- Automata and Formal Language Theory
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Keyword
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Itaru KATAOKA, Tetsuo MORIYA, "d-Primitive Words and D(1)-Concatenated Words" in IEICE TRANSACTIONS on Information,
vol. E92-D, no. 8, pp. 1577-1579, August 2009, doi: 10.1587/transinf.E92.D.1577.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.E92.D.1577/_p
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@ARTICLE{e92-d_8_1577,
author={Itaru KATAOKA, Tetsuo MORIYA, },
journal={IEICE TRANSACTIONS on Information},
title={d-Primitive Words and D(1)-Concatenated Words},
year={2009},
volume={E92-D},
number={8},
pages={1577-1579},
abstract={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.},
keywords={},
doi={10.1587/transinf.E92.D.1577},
ISSN={1745-1361},
month={August},}
Copy
TY - JOUR
TI - d-Primitive Words and D(1)-Concatenated Words
T2 - IEICE TRANSACTIONS on Information
SP - 1577
EP - 1579
AU - Itaru KATAOKA
AU - Tetsuo MORIYA
PY - 2009
DO - 10.1587/transinf.E92.D.1577
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E92-D
IS - 8
JA - IEICE TRANSACTIONS on Information
Y1 - August 2009
AB - 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.
ER -
English
