Equivalence of regular binoid expressions and regular expressions denoting binoid languages over free binoids

Kosaburo Hashiguchi, Naoto Sakakibara, Shuji Jinbo

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

A free binoid Σ*(○,•) over a finite alphabet Σ is a free algebra generated by Σ with two independent associative operators, ○ and •. It has also the same identity λ to both operations. Any element of Σ*(○,•) is denoted uniquely by a sequence of symbols from the extended alphabet E(Σ)=Σ∪{○,•,(,)}, and any subset of a free binoid is called a binoid language. The set of regular binoid expressions are introduced so that all languages denoted by regular binoid expressions are those which contain finite binoid languages, and closed under five operations, ∪,○-concatenation, •-concatenation, ○-closure and •-closure. It is shown that for any regular (monoid) expression denoting a binoid language R, there exists a regular binoid expression denoting R. This result together with the main result in a previous paper implies that the class of binoid languages denoted by binoid regular expressions is the same as the class of binoid languages denoted by regular expressions over free binoids.

Original languageEnglish
Pages (from-to)251-266
Number of pages16
JournalTheoretical Computer Science
Volume312
Issue number2-3
DOIs
Publication statusPublished - Jan 30 2004

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Regular Expressions
Algebra
Mathematical operators
Equivalence
Concatenation
Closure
Free Algebras
Monoid
Language
Imply
Closed
Subset
Operator

Keywords

  • Free binoid
  • Regular (monoid) expression
  • Regular binoid expression
  • Regular language

ASJC Scopus subject areas

  • Computational Theory and Mathematics

Cite this

Equivalence of regular binoid expressions and regular expressions denoting binoid languages over free binoids. / Hashiguchi, Kosaburo; Sakakibara, Naoto; Jinbo, Shuji.

In: Theoretical Computer Science, Vol. 312, No. 2-3, 30.01.2004, p. 251-266.

Research output: Contribution to journalArticle

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