More on the Descriptional Complexity of Products of Finite Automata

We investigate the descriptional complexity of the nu(i)- and alpha(i)-products with 0 <= i <= 2 of two automata, for reset, permutation, permutation-reset, and finite automata in general. This is a continuation of the recent studies on the state complexity of the well-known cascade product undertaken in [7, 8]. Here we show that in almost all cases, except for the direct product (nu(0)) and the cascade product (alpha(0)) for certain types of automata operands, the whole range of state complexities, namely the interval [1, nm], where n is the state complexity of the left operand and m that of the right one, is attainable. To this end we prove a simulation result on products of automata that allows us to reduce the products and automata in question to the nu(0), alpha(0), and a double sided alpha(0)-product.