Converting NFAs to DFAs

Question

I wanted to find the diagram for the DFA that recognizes $$L=\{w \mid w \text{ starts with }1 \text{ and ends with }0\}$$ Clearly, it is easier to find a NFA first. But I couldn't convert it to a DFA with the method my textbook suggested. What went wrong? The DFA that resulted from taking all the subsets of states from the NFA and drawing and pruning the extra arrows doesn't recognize $L$.

Answer 1

I don't know what method your textbook suggests or how you applied it but I think you just want to do the following

• $q_{\rm start}[1 \to q_1]$
• $q_1[1 \to q_1, 0 \to q_0]$
• $q_0[1 \to q_1, 0 \to q_0]$ (accepting)

Answer 2

It's not quite clear what your NFA translation algorithm is, but here is a diagram of the DFA you are looking for.