NFA to DFA where a state only has an epsilon transition

Question

If when converting the NFA table to the DFA table there is a state that only as an epsilon transition, how is it converted onto the DFA table.

For example if state 1 only accepts 2 in the ε column, how will it look in the DFA conversion?

Transition table:

     a     b     c    ε
1   {}    {}    {}   {2}
2   {3}   {}    {}   {}
3   {4}   {3,4} {}   {}
4   {4}   {}    {}   {}

Answer 1

I think it's better if you first eliminate epsilon transition to get NFA (without epsilon transition). From NFA it should be easier to get the equivalent DFA.

How to eliminate epsilon transition?

First, we have term ECLOSE of a state. ECLOSE(q) is defined as set of all states (including state q itself) that can be reached by following epsilon transition. In your case:

ECLOSE(1) = {1,2}

To eliminate epsilon transition, follow below steps:

1. If ECLOSE(1) contains the final state, then set state 1 as final state
2. Add transition (with respective label) from state 1 to state q if and only if there is a transition from some states in ECLOSE(1) to state q
3. Now you can remove all epsilon transitions.

After above steps (you didn't specify which states are start and or final states), you should get:

    a     b     c    
1   {3}   {}    {}   
2   {3}   {}    {}   
3   {4}   {3,4} {}   
4   {4}   {}    {}