I'm doing a homework assignment for my theory of computation class and am a bit confused how to combine 2 DFAs. The book says it uses the "intersection construction" to do so, but I'm not sure what that is. Here are 2 examples:
The idea is pretty straightforward, although I can see where the confusion comes in. I will give a text/symbolic description of the process for making the intersection (union, difference) machines via the Cartesian Product Machine construction (same thing as you are talking about).
A DFA is a 5-tuple (E, Q, q0, A, f) where
Say we have two machines M' = (E', Q', q0', A', f') and M'' = (E'', Q'', q0'', A'', f''). To make the discussion easier, we assume E' = E''. We will now construct M''' so that L(M''') = L(M') intersect (or union or difference) L(M'').
There you go! Let's now consider two machines: one which accepts a^2n, and one which accepts a^3n (the intersection should be a machine accepting a^6n... right?).
For M', we have...
For M'', we have...
For M''', we get...
And there you go! Please let me know if this needs clarification.