# Are Nondeterministic Finite Automata not allowed 'sink-states'?

By definition are Nondeterministic Finite Automata not allowed a 'sink-state' (non-accepting state we don't get out of)? I can see us having them for NFA but not necessary but do not see how they are against the rules of a NFSA/NFA or should not be allowed. My teacher said they are not allowed in a NFA/NFSA, but even if you have a 'sink state' in a NFA/NFSA I can see the diagram working and meeting the conditions. Can someone please clarify about this.

It's also worth noting that NFA and DFA construction algorithms based on Brzozowski derivatives often naturally generate these sink states. See, for example, figure 2 in this tech report. Rather than detect them directly (which isn't difficult), you can remove these states with DFA minimisation if you were going to perform that step anyway. In fact, you can add a known sink state with no incoming transitions $$q_\mathrm{sink}$$ to the non-minimised DFA, perform minimisation, and then any state merged with $$q_\mathrm{sink}$$ must also be a sink state and can be safely removed.