algebra universalis

, Volume 33, Issue 1, pp 98–126 | Cite as

Notes on equational theories of relations

  • S. L. Bloom
  • Z. Ésik
  • Gh. Stefanescu


We describe explicitly the free algebras in the equational class generated by all algebras of binary relations with operations of union, composition, converse and reflexive transitive closure and neutral elements 0 (empty relation) and 1 (identity relation). We show the corresponding equational theory is decidable by reducing the problem to a question about regular sets. Similar results are given for two related equational theories.


Binary Relation Equational Theory Transitive Closure Free Algebra Identity Relation 
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Copyright information

© Birkhäuser Verlag 1995

Authors and Affiliations

  • S. L. Bloom
    • 1
  • Z. Ésik
    • 1
  • Gh. Stefanescu
    • 1
  1. 1.Computer Science DepartmentA. József UniversitySzegedHungary

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