I have been given the following NFA:
and, using the conversion algorithm (creating a new event for every union of events), I came up with the following DFA (note: I added here the events from the NFA, even if they are never accessed, for clarity on how the union events are formed):
However, I can clearly see that something is wrong: the NFA rejects the string "ababa", yet my DFA accepts it. The transition $\delta^*(\{A,C,D\},a)$ returns the event $\{A,B,D\}$, an accepting state. Through sheer intuition, I imagine it should instead return the event $\{A,B\}$, but I don't quite see what went wrong. I've redone this multiple times, each time with the same result. What I am doing wrong in my application of the theorem?
The NFA accepts the string "ababa":
A -> A -> A -> B -> C -> D
Remember that an NFA accepts if there is some path which leads to an accepting state.