Automata resulting from graph operations

The binary operations like Cartesian products, normal and lexicographic products on graphs have played a vital role in graph construction. An insight of automata as directed graphs motivated us to study some of these products on these abstract machines. In this paper we operate normal and lexicographic products over automata and analyze the language recognized by these resultant automata. It is observed that the Generalized Parikh vectors of the language of the resultant automata are a family of parallel lines in the two dimensional plane. The lexicographic product of path automata appears as a neural network after a few modifications using reactive automata.