How to convert the following from NFA with ε-moves to DFA?

Question

Can you provide the transition table along with the solution for better understanding?

Answer 1

It helps to begin by asking: What language does this NFA recognize? There are two distinct pathways, one that recognizes (10)* (including the empty string) and one that recognizes 0* (again, including the empty string).

To build a DFA for this language, it helps to try to describe what you know about the string seen so far, then add a state to the DFA for every piece of information. There is no single solution. For example, one key observation is that the first symbol (0 or 1) determines the type of acceptable string, 0* or (10)*. Therefore:

1. We need an initial state A, which should also be an accepting state since the empty string is valid.
2. On a 0, we go to a state B that consumes additional 0's.
3. On a 1, we alternate between two states C and D that consume 0's and 1's respectively.

For example, state C means „I have seen a 1 and I expect to see a 0”.

It is important to define every transition for every (state,symbol) combination. In our case, strings like 00001 or 10101011 should move to an error state E, which should be absorbing (no escape).

state	accepting	on 0 go to	on 1 go to
A	yes	B	C
B	yes	B	E
C	no	D	E
D	yes	E	C
E	no	E	E