automatafinite-automatacomputation-theorydfaautomata-theory

Can the unreachable state removed in this minimized DFA?


So this is the DFA in the question needs to be minimzed

So this is the DFA to be minimized

The answer to this question is this and as you can see the DFA is minimized now.

enter image description here

My question is : as you can see the minimized DFA has a state q7 which is unreachable from the start or initial state. So why they are showing state q7 in the final answer, shouldn't the unreachable state be removed to make this dfa even more minimized.


Solution

  • If you look carefully none of the states q4,q5,q6,q7 are reachable from the initial state q0, not just q7, so all these 4 states should be removed. my solution for this would start from q0,q1,q2,q3, and then follow the procedure of reduction.

    This is what I think the answer should be: image link