On equations for union-free regular languages

Siniša Crvenković, Igor Dolinka, Zoltán Ésik

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

In this paper we consider the variety script U sign script F sign generated by all algebras of binary relations equipped with the operations of composition, reflexive-transitive closure, and the empty set and the identity relation as constants. This variety coincides with the variety generated by the union-free reducts of Kleene algebras of languages and its free objects are formed by union-free regular languages, that is, regular languages represented by regular expressions having no occurrence of +. We show that the variety script U sign script F sign is not finitely based. The situation does not change if we consider the variety script U sign script F sign generated by the above algebras of binary relations equipped with the conversion operation.

Original languageEnglish
Pages (from-to)152-172
Number of pages21
JournalInformation and Computation
Volume164
Issue number1
DOIs
Publication statusPublished - Jan 10 2001

Keywords

  • Equational logic
  • Kleene algebra
  • Regular language

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Computer Science Applications
  • Computational Theory and Mathematics

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