Abstract
A bisemigroup consists of a set of elements and two associative operations. A bimonoid is a bisemigroup which has an identity to each associative operation. A binoid is a bimonoid which has the same identity to the two associative operations. In a previous paper, we introduced these three notions, and studied formal languages over free binoids (which are subsets of a free binoid where any element of a free binoid is denoted by its standard form which is a sequence of symbols). In this paper, we introduce a class of expressions called regular binoid expressions and show that any binoid language denoted by a regular binoid expression can be regarded to be a set of the standard forms of elements of a free binoid which can be recognized as a regular (monoid) language.
| Original language | English |
|---|---|
| Pages (from-to) | 291-313 |
| Number of pages | 23 |
| Journal | Theoretical Computer Science |
| Volume | 304 |
| Issue number | 1-3 |
| DOIs | |
| Publication status | Published - Jul 28 2003 |
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Keywords
- Binoids
- Regular binoid expressions
- Regular languages
- Right linear grammars
ASJC Scopus subject areas
- Computational Theory and Mathematics
Cite this
Regular binoid expressions and regular binoid languages. / Hashiguchi, Kosaburo; Wada, Yoshito; Jinbo, Shuji.
In: Theoretical Computer Science, Vol. 304, No. 1-3, 28.07.2003, p. 291-313.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Regular binoid expressions and regular binoid languages
AU - Hashiguchi, Kosaburo
AU - Wada, Yoshito
AU - Jinbo, Shuji
PY - 2003/7/28
Y1 - 2003/7/28
N2 - A bisemigroup consists of a set of elements and two associative operations. A bimonoid is a bisemigroup which has an identity to each associative operation. A binoid is a bimonoid which has the same identity to the two associative operations. In a previous paper, we introduced these three notions, and studied formal languages over free binoids (which are subsets of a free binoid where any element of a free binoid is denoted by its standard form which is a sequence of symbols). In this paper, we introduce a class of expressions called regular binoid expressions and show that any binoid language denoted by a regular binoid expression can be regarded to be a set of the standard forms of elements of a free binoid which can be recognized as a regular (monoid) language.
AB - A bisemigroup consists of a set of elements and two associative operations. A bimonoid is a bisemigroup which has an identity to each associative operation. A binoid is a bimonoid which has the same identity to the two associative operations. In a previous paper, we introduced these three notions, and studied formal languages over free binoids (which are subsets of a free binoid where any element of a free binoid is denoted by its standard form which is a sequence of symbols). In this paper, we introduce a class of expressions called regular binoid expressions and show that any binoid language denoted by a regular binoid expression can be regarded to be a set of the standard forms of elements of a free binoid which can be recognized as a regular (monoid) language.
KW - Binoids
KW - Regular binoid expressions
KW - Regular languages
KW - Right linear grammars
UR - http://www.scopus.com/inward/record.url?scp=0038148894&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0038148894&partnerID=8YFLogxK
U2 - 10.1016/S0304-3975(03)00137-3
DO - 10.1016/S0304-3975(03)00137-3
M3 - Article
AN - SCOPUS:0038148894
VL - 304
SP - 291
EP - 313
JO - Theoretical Computer Science
JF - Theoretical Computer Science
SN - 0304-3975
IS - 1-3
ER -