# Understanding NFA (nondeterministic finite automaton) with a null transition

I'm reading Computer Science: An Interdisciplinary Approach. It mentioned an NFA (nondeterministic finite automaton) with a null transition, as shown above, recognizes all binary strings that do not contain bba as a substring.

I didn't quite understand why it says so. If the null transition happens before reading the bba, it stuck at state 2 and will report yes at the end?

So, in your example, if the automaton makes the null transition, it can read $$bb$$ while staying in state $$2$$. But when it reads the $$a$$, it has no legal transition so that run rejects. Any run that stays in states $$0$$ and $$1$$ must also reject, because those two states are rejecting states. Therefore, the automaton does indeed reject all strings containing $$bba$$.
• safaribooksonline.com/library/view/computer-science-an/… In the above example, the author says it will accept ababb because we can establish the sequence of state transitions as 0-0-1-0-2-2-2. But this is not deterministic, it is only one possible result, right? – Qiang Huang Sep 28 '18 at 17:03