On \(\alpha{}_ 0-\nu{}_ 1\)-products of automata (Q1814100)

A comparison of various types of product of automata (studied especially by the first author): \(\alpha_ 0\)-products, \(\nu_ 1\)-products, \(\alpha_ 0\)-\(\nu_ 1\)-products) is exposed. By a traditional for universal algebras way some operators for automata are constructed. On this base classes of automata, closed under one or several of these operators are characterized. The main result (Theorem 3.6) is the identity of the homomorphic images of \(\alpha_ 0\)-\(\nu_ 1\)-products and the general products if infinite products ar permitted. A detailed analysis of the situation when only finite products are allowable is provided.