How to find the intersection of two NFA

Question

In DFA we can do the intersection of two automata by doing the cross product of the states of the two automata and accepting those states that are accepting in both the init

Answer 1

An alternative to constructing the product automaton is allowing more complicated acceptance criteria. Ordinarily, an NFA accepts an input string when it has reached any one of a set of accepting final states. That can be extended to boolean combinations of states. Specifically, you construct the automaton for the intersection like you do for the union, but consider the resulting automaton to accept an input string only when it is in (what corresponds to) accepting final states in both automata.