Acceptance conditions are properties of states, i.e., the acceptance condition of a safety automaton is a set of states which we call the safe states. Hence, if the acceptance condition is G phi, then the states satisfying phi are the safe ones and those satisfying !phi are the unsafe one.

There are also omega-automata where acceptance conditions refer to transitions instead of states (we actually use these for the translation from LTL to omega automata), but these automata are not more powerful than the traditional ones where acceptance conditions are defined on state sets only.