Consider two automata A1 and A2 defined over an alphabet Σ whose languages are LA1 and LA2 , respectively.
The synchronous product (more briefly, product) of A1 and
A2 is an automaton over the alphabet Σ whose language is
LA1 ∩ LA2 . The language of such a product is the intersection
of the languages of A1 and A2. The product of more than two
automata is defined as an iteration of products of two automata.
Many references on automata theory can be consulted for more
detail, such as [14], [15].