# What to do with empty set during NFA to DFA conversion?

I am currently converting this NFA to a DFA

I have come up with the following DFA:

        0      1
->A    {A}    {B}
B    {CA}
*CA    {A}    {AB}
AB    {CA}   {B}


Although, I have no idea what to put for B. In the NFA, upon the B receiving 1 input, it goes nowhere - assumable unaccepted by the NFA. Do I send the DFA to a new, dead state upon receiving input 1 whilst in B?

I can try it:

        0      1
->A    {A}    {B}
B    {CA}   {}
*CA    {A}    {AB}
AB    {CA}   {B}
{}    {}     {}


But is this correct by the rules of DFA?

• Have you tried that? Did it work? By the way, can you give a reference to or name the way you convert NFA to DFA? – John L. Nov 22 '18 at 5:22
• Sorry, I am using Subset Construction Method. – NBray Nov 22 '18 at 5:26

According to the subset construction, the state you go to from state $$\{B\}$$ when you read character $$1$$ is the set of all states that the original NFA can go to when it's in one of the states in $$\{B\}$$ (i.e., it's in state $$B$$) reads $$1$$. This set of states is $$\emptyset$$, since the NFA has no transitions from $$B$$ for symbol $$1$$.
So this actually answers both of your questions at once: it's what you do with $$\emptyset$$ and it's the dead state you need (you can check from the definition that $$\emptyset$$ really is a dead state in the DFA.