### 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 |
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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