The variety of Kleene algebras with conversion is not finitely based

S. Crvenković, I. Dolinka, Z. Ésik

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

Given an arbitrary set A, one obtains the full Kleene algebra of binary relations over A by considering the operations of union, composition, reflexive-transitive closure, conversion, and the empty set and the identity relation as constants. Such algebras generate the variety of Kleene algebras (with conversion). As a result of a general analysis of identities satisfied by varieties having an involution operation, we prove that the variety of Kleene algebras with conversion has no finite equational axiomatization. In our argument we make use of the fact that the variety of Kleene algebras without conversion is not finitely based and that, relatively to this variety, the variety of Kleene algebras with conversion is finitely axiomatized.

Original languageEnglish
Pages (from-to)235-245
Number of pages11
JournalTheoretical Computer Science
Volume230
Issue number1-2
DOIs
Publication statusPublished - Jan 6 2000

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Fingerprint Dive into the research topics of 'The variety of Kleene algebras with conversion is not finitely based'. Together they form a unique fingerprint.

  • Cite this