I'm currently teaching myself Automaton using Peter Linz book - An Introduction to Formal Languages and Automata 4th edition. While reading chapter 2 about NFA, I was stuck this example (page 51):
According to the author, the transition function $\delta^{*}(q_1,a) = \{q_0, q_1, q_2\}$, and I have no idea how this works since the definition is defined in the book as following:
For an nfa, the extended transition function is defined so that $\delta^{*}(q_i,w)$ contains $q_j$ if and only if there is a walk in the transition graph from $q_i$ to $q_j$ labeled $w$. This holds for all $q_i, q_j \in Q$ and $w \in \sum^{*}.$
From my understanding, there must be a walk of label $a$ so that a state $q_k$ will be in the set. In the example above, there is no such walk label $a$ from $q_1$ to $q_0, q_2$. Perhaps, I missed some important points, but I honestly don't understand how the author got that answer, i.e. $\{q_0, q_1, q_2\}$. Any suggestion?
Thank you,
Note I already posted this question as I already posted my question at https://cstheory.stackexchange.com/questions/7009/how-to-compute-the-transition-function-in-non-determinism-finite-accepter-nfa. However, it was closed because it's not at graduate research level.