The diagram below the state diagram and its breakpoint construction.
My question is why do we not have a transition from q2 to q3 with input 'a'. Since the successor of q2 with 'a' is also q3. In that case, would we have transition from q2 to q3 with both 'a' and 'b' and hence '*' as input there?
In short, my question is, would it be valid to replace the green highlighted 'b' input with a '*' ?
Also, are we supposed to check transitions for all input combinations? i.e. in this case would be !a&!b, !a&b, a&!b, a&b