Regular binoid expressions and regular binoid languages

  • Authors:

  • Kosaburo Hashiguchi;Yoshito Wada;Shuji Jimbo

  • Affiliations:

  • Department of Information Technology, Faculty of Engineering, Okayama University, 1-1, Tsushima-Naka, 3-chome, Okayama 700-0082, Japan;Department of Information Technology, Faculty of Engineering, Okayama University, 1-1, Tsushima-Naka, 3-chome, Okayama 700-0082, Japan;Department of Information Technology, Faculty of Engineering, Okayama University, 1-1, Tsushima-Naka, 3-chome, Okayama 700-0082, Japan

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2003

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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.