Axiomatizing Shuffle and Concatenation in Languages

Stephen L. Bloom, Zoltán Ésik

Research output: Contribution to journalArticle

12 Citations (Scopus)


We consider the variety Lang generated by all language structures (PΣ, ·, ⊗, +, 0, 1), and the variety Lg of ordered algebras generated by the structures (PΣ, ·, ⊗, 0, 1, ⊆), where PΣ is the powerset of Σ*, and where B · C is the complex concatenation of the languages B, C ⊆ Σ*, B ⊗ C is their shuffle product, and B + C is their union. We prove that for each finite set E of equations valid in Lang there is a (finite) model SE of E in which some inequation valid in Lg fails. It follows that neither variety is finitely axiomatizable.

Original languageEnglish
Pages (from-to)62-91
Number of pages30
JournalInformation and Computation
Issue number1
Publication statusPublished - Nov 25 1997


ASJC Scopus subject areas

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

Cite this