On commutative asynchronous nondeterministic automata

Abstract

In this paper, we deal with nondeterministic automata, in particular, commutative asynchronous ones. Our goal is to give their isomorphic representation under the serial product or equivalently, under the α0-product. It turns out that this class does not contain any finite isomorphically complete system with respect to the α0-product. On the other hand, we present an isomorphically complete system for this class which consists of one monotone nondeterministic automaton of three elements.