Nonfinite axiomatizability of the equational theory of shuffle

Z. Ésik, Michael Bertol

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10 Citations (Scopus)

Abstract

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
Volume35
Issue number6
Publication statusPublished - Jun 1998

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Algebra

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  • Information Systems

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Nonfinite axiomatizability of the equational theory of shuffle. / Ésik, Z.; Bertol, Michael.

In: Acta Informatica, Vol. 35, No. 6, 06.1998, p. 505-539.

Research output: Contribution to journalArticle

Ésik, Z. ; Bertol, Michael. / Nonfinite axiomatizability of the equational theory of shuffle. In: Acta Informatica. 1998 ; Vol. 35, No. 6. pp. 505-539.
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