### Abstract

The axioms of iteration theories, or iteration categories, capture the equational properties of fixed point operations in several computationally significant categories. Iteration categories may be axiomatized by the Conway identities and identities associated with finite automata. We show that the Conway identities and the identities associated with the members of a subclass of finite automata is complete for iteration categories iff for every finite simple group G there is an automaton Q âsuch that G is a quotient of a group in the monoid M(Q) of the automaton Q. We also prove a stronger result that concerns identities associated with finite automata with a distinguished initial state.

Original language | English |
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Pages (from-to) | 54-69 |

Number of pages | 16 |

Journal | Mathematical Structures in Computer Science |

Volume | 27 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2017 |

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### ASJC Scopus subject areas

- Mathematics (miscellaneous)
- Computer Science Applications