### 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 language | English |
---|---|

Pages (from-to) | 505-539 |

Number of pages | 35 |

Journal | Acta Informatica |

Volume | 35 |

Issue number | 6 |

Publication status | Published - Jun 1998 |

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### ASJC Scopus subject areas

- Information Systems

### Cite this

*Acta Informatica*,

*35*(6), 505-539.

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

Research output: Contribution to journal › Article

*Acta Informatica*, vol. 35, no. 6, pp. 505-539.

}

TY - JOUR

T1 - Nonfinite axiomatizability of the equational theory of shuffle

AU - Ésik, Z.

AU - Bertol, Michael

PY - 1998/6

Y1 - 1998/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0041169733&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041169733&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0041169733

VL - 35

SP - 505

EP - 539

JO - Acta Informatica

JF - Acta Informatica

SN - 0001-5903

IS - 6

ER -