Axiomatizing iteration categories

Z. Ésik1 2

Dedicated to Ferenc Gécseg on his 60th birthday

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.

Footnotes:

  1 Supported in part by grant no. T22423 of the National Science Foundation of Hungary, the US-Hungarian Joint Fund under grant no. 351, and by the Austrian-Hungarian Action Foundation.

  2 Department of Computer Science A. József University Árpád tér 2. 6720 Szeged Hungary