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  • $\begingroup$ That does not find all useless states: some may be reachable from $q_0$, but as long as you can't reach a final state from there they're useless. $\endgroup$ Commented Sep 28, 2017 at 16:49
  • $\begingroup$ @Raphael Huh? The question defines "useless" as meaning "never entered on any input string" not "never entered on any accepted input string." You're welcome to argue that states from which no accepting state is reachable can also be optimized away, but that's not what this question is asking about. $\endgroup$ Commented Sep 28, 2017 at 22:18
  • $\begingroup$ @DavidRicherby True, my bad. $\endgroup$ Commented Sep 29, 2017 at 4:47