I am working with converting an NFA to a DFA and came across an odd set notation issue that I don't know how to answer.
Say I have the following NFA and assume the starting state to be zero:
So if I let q0 = A, q1 = B, q2 = C then B is my only accepted state.
Looking at all 3 states with transitions 0 and 1 I find transition 0 to be the following
A -> {A,B}
B -> {C}
C -> {emptyset}
With Transition 1 I get the following:
A -> {B}
B -> {C}
C -> {C}
so in my DFA A takes me to state {AB} an accepting state with 1 or {B} also an accepting state with 0 and I need to carry on to minimize the states.
Eventually I end up with the following with transition 0:
{ABC} -> {A,B,C,NULL}.
Can I translate this into $A$ or $B$ or $C$ or $\emptyset$?
I believe you must have encountered a state which has no transition specified for a particular input symbol. As for your question yes you can take the union(OR) of Sets with NULL $\space\emptyset$ which is nothing but the non-empty set itself. For example : $$\{q1 , q2 ,q0\}\cup\{\emptyset\} = \{q1 , q2 ,q0\}$$