So, by the Bzozowski theorem, if A is DFA det(rev(det(rev(A))) would have minimal number of states. And for the most of them work. But for this example, I can't figure out why it doesn't. I have an DFA which is NOT minimal (the min. automata have 2 states ) but det(rev(A)) is the same automata (obviously det(rev(det(rev(A))) is also the same). Can you tell me what am I doing wrong ? Tnx.
Your initial automaton has two final states. Its reverse should have two initial states. You wanted to avoid that, and added a new initial state.
The proper construction just uses the two initial states. The determinization algorithm can handle that.