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Equational axioms associated with finite automata for fixed point operations in cartesian categories

Published online by Cambridge University Press:  08 April 2015

ZOLTÁN ÉSIK
ZOLTÁN ÉSIK*
Affiliation:
Department of Computer Science, University of Szeged, Árpád tér 2, 6720 Szeged, Hungary Email: [email protected]
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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 $\mathcal{Q}$ of finite automata is complete for iteration categories iff for every finite simple group G there is an automaton Q ∈ $\mathcal{Q}$ such 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.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 27 , Issue 1 , January 2017 , pp. 54 - 69
Copyright
Copyright © Cambridge University Press 2015 

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