I've run into a problem concerning epsilon transitions and removing them. Specifically, it is to do with the picture seen in this post. My problem is that I am unsure of what to do with q1. I've already attempted to solve it but I don't know if it's correct. Should it just sit there still with no inputs going to it essentially making it a dead state? What should its loop be that was once an epsilon loop?
In the original automaton, there is no way to be in $q_1$, read one symbol, and end up in $q_1$, so in the resulting automaton, there is no loop on $q_1$.
There won't be a loop over $q_1$ but there will be a transition $q_1\in\delta(q_0,0)$, so it won't be dead state.