Group theoretic characterization of linear permutation automata

摘要

In this paper we characterize all permutation automata which can be linearly realized over the field GF(p) in terms of the group generated by the automaton. From this group theoretic characterization of linear permutation automata we derive, among other results, a complete characterization of all homomorphisms of a linear automaton which yield linearly realizable image automata as well as several results about the structure of linear automata.