### 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

*Theoretical Computer Science*,

*304*(1-3), 291-313. https://doi.org/10.1016/S0304-3975(03)00137-3

**Regular binoid expressions and regular binoid languages.** / Hashiguchi, Kosaburo; Wada, Yoshito; Jinbo, Shuji.

Research output: Contribution to journal › Article

*Theoretical Computer Science*, vol. 304, no. 1-3, pp. 291-313. https://doi.org/10.1016/S0304-3975(03)00137-3

}

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 -