When can a Non-Deterministic Finite Automaton with Epsilon transitions considered to be in an accepted state?


A non-deterministic finite automaton is considered to be halted when either the whole input string has been consumed or when we reach a state where no available transition (if any) matches the current character being read.

If the machine halts when it’s in an accepted state and at the same time the whole input has been consumed the input string is considered to be accepted.

Now, when introduce $ \epsilon$ transitions the machine doesn’t necessarily halt when the whole input string has been consumed, for it is possible that there are still $ \epsilon$ transitions available.

Suppose we have a NFA that is in an accepted state and also that the whole input has been consumed, but there are still $ \epsilon$ transitions available in this state, can we considered the input string to be accepted or do we need to "follow the trail" of $ \epsilon$ transitions until we reach a state where no other transition is available?