I have this NFA:
1,{2, 3}
2,empty
3,{4}
4,empty
All the arrows in this NFA are epsilon-arrows.
I understand that all possible states that can be reached from each of the states, using only epsilon paths are these:
E(1) = {1,2,3,4}
E(2) = {2}
E(3) = {3,4}
E(4) = {4}
However I don't understand how this state set was achieved:
DFA = {empty, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2,
3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}
My understanding is that the transition table that looks like this:
epsilon
1 2, 3
2 -
3 4
4 -
is to be used to determine the DFA, along with the E function.
I tried to do it like this:
Start state = 1 => the Result = {E(1)} = {{1, 2, 3, 4}}
T({1, 2, 3, 4}) = E(transitionTable({1, 2, 3, 4})) = E({2, 3, 4}) = {2, 3, 4}
Result = {{1, 2, 3, 4}, {2, 3, 4}}
T({2, 3, 4}) = E({4}) = {4}
Result = {{1, 2, 3, 4}, {2, 3, 4}, {4}}
T({4}) = E({}) = {}
Result = {{1, 2, 3, 4}, {2, 3, 4}, {4}, {}}
What am I doing wrong here? Any help is appreciated.