### Abstract

We associate an identity with every finite automaton and show that a set of equations consiting of some classical identities as well as the equations associated with a subclass of finite automata is complete for iteration theories if and only if every finite simple group divides the semigroup of an automaton in the given subclass. By taking a special subclass with this property, we arrive at the final result of the paper.

Original language | English |
---|---|

Pages (from-to) | 65-82 |

Number of pages | 18 |

Journal | Acta Cybernetica |

Volume | 14 |

Issue number | 1 |

Publication status | Published - 1999 |

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### ASJC Scopus subject areas

- Hardware and Architecture
- Software

### Cite this

**Axiomatizing iteration categories.** / Ésik, Z.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Axiomatizing iteration categories

AU - Ésik, Z.

PY - 1999

Y1 - 1999

N2 - We associate an identity with every finite automaton and show that a set of equations consiting of some classical identities as well as the equations associated with a subclass of finite automata is complete for iteration theories if and only if every finite simple group divides the semigroup of an automaton in the given subclass. By taking a special subclass with this property, we arrive at the final result of the paper.

AB - We associate an identity with every finite automaton and show that a set of equations consiting of some classical identities as well as the equations associated with a subclass of finite automata is complete for iteration theories if and only if every finite simple group divides the semigroup of an automaton in the given subclass. By taking a special subclass with this property, we arrive at the final result of the paper.

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UR - http://www.scopus.com/inward/citedby.url?scp=24244454475&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:24244454475

VL - 14

SP - 65

EP - 82

JO - Acta Cybernetica

JF - Acta Cybernetica

SN - 0324-721X

IS - 1

ER -