A DFA state represents a set of possible ATN configurations. As Aho, Sethi, Ullman p. 117 says "The DFA uses its state to keep track of all possible states the ATN can be in after reading each input symbol. That is to say, after reading input a1a2..an, the DFA is in a state that represents the subset T of the states of the ATN that are reachable from the ATN's start state along some path labeled a1a2..an." In conventional NFA→DFA conversion, therefore, the subset T would be a bitset representing the set of states the ATN could be in. We need to track the alt predicted by each state as well, however. More importantly, we need to maintain a stack of states, tracking the closure operations as they jump from rule to rule, emulating rule invocations (method calls). I have to add a stack to simulate the proper lookahead sequences for the underlying LL grammar from which the ATN was derived.