I've been tasked with converting an NFA to a DFA in diagram form.
The NFA is like so: NFA
And my DFA:Updated DFA
I have the nagging feeling that I'm missing something in the conversion regarding {1,2} and 'a' how the epsilon and move from the starting set of states to {2} or {3}. My textbook describes the general algorithm for the conversion, and that's how I arrived at the set of sets of active states that became nodes for the DFA, but it doesn't show how exactly a DFA from an NFA would look, so I'm looking for clarity. Is this DFA a correct representation of the NFA? And if not, where did I conceptually falter?
Edit: Updated the DFA diagram, there was one mistake when transcribing from paper. I still have the same questions!
I believe this to be the full and correct diagram. Thank you saulspatz for spotting the missing transition - the diagram below includes a transition from state 3 to itself when b is the input.
Proper DFA