Two finite state automatons can be combined, resulting in one larger finite state automaton.
State can be represented as graph, with states (dots) and transition functions (arrows).
Just combine states from two graphs into state pairs using Cartesian Multiplier (each with each), represent each pair as single node, then connect state pairs with transition functions properly.
Then this complex automaton can be reduced, by removing duplicate transition functions (arrows).
This process (Combining State) can be repeated as many times as is needed.
(this has use in mapping 'Stitie Turing Machine' into Turing Machine).