I have a task to determine the upper bound of states in the Minimal Deterministic Finite Automata that recognizes the language: $ L(A_1) \backslash L(A_2) $, where $ A_1 $ is a Deterministic Finite Automata (DFA) with $n$ states and $A_2$ is Non-deterministic Finite Automata (NFA) with $m$ states.
The way I am trying to solve the problem:
- $ L(A_1) \setminus L(A_2) = L(A_1) \cap L(\Sigma^* \backslash L(A_2))$, which is language, that is recognised by an automaton $L'$ with $nm$ states.
- Determinization of $L'$ which has $(nm)^2$ states and it is the upper bound of states.
Am I right?