Nonfinite axiomatizability of the equational theory of shuffle

Zoltán Ésik, Michael Bertol

Research output: Contribution to journalArticle

10 Citations (Scopus)


We consider language structures L = (P, ·, ⊗, +, 1, 0), where P consists of all subsets of the free monoid ∑*; the binary operations ·, ⊗ and + are concatenation, shuffle product and union, respectively, and where the constant 0 is the empty set and the constant 1 is the singleton set containing the empty word. We show that the variety Lang generated by the structures L has no finite axiomatization. In fact we establish a stronger result: The variety Lang has no finite axiomatization over the variety of ordered algebras Lg generated by the structures (P, ·, ⊗, 1, ⊆), where ⊆ denotes set inclusion.

Original languageEnglish
Pages (from-to)505-539
Number of pages35
JournalActa Informatica
Issue number6
Publication statusPublished - Jun 1998

ASJC Scopus subject areas

  • Software
  • Information Systems
  • Computer Networks and Communications

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