I can't understand why $\epsilon$ is accepted. I thought if $\epsilon$ is inputed then it would go from $q_1$ to $q_3$. $a$ is also accepted, but I though if $a$ is inputed then then the NFA would die, because in $q_1$ there's no where to go.
I read on another post about $\epsilon$ being at two states at the same time, but couldn't get it. What exactly is happening when $\epsilon$ is entered and when $a$ is entered (two different strings)?
q1 epsilon--------------------- q1 q3
I think the above is the correct tree when $\epsilon$ is inputed, but makes no sense to me.