# DFA Minimization

I am currently in a class that deals with DFA's and their minimization. However I believe I have reached a DFA where the method of minimization we were taught doesn't work.

I have the following DFA (in JFLAP)

Using the method given in class I do the following see if their are any non dissimilar states and if so collapse them together.

 | q0  q1  q2  q3  q4  q5
-------------------------
a| q1  q1  q2  q3  q4  q5
b| q3  q2  q5  q4  q5  q5


However there are no states where both a and b go to the same state, therefore no collapse states.

However when doing it in JFLAP it gives the following

The only way I can see you getting what JFLAP does is just thinking and having to realize bother q1 and q3 can be joined as well as q2 and q4.

• What's your question? – David Richerby Apr 2 '15 at 21:01
• How is this a DFA given that state initial state q0 has two transitions for an input symbol a? – user4275686 Apr 2 '15 at 21:58
• The a near q3 is going from q3 to q3. – Zimm3r Apr 2 '15 at 23:58
• @DavidRicherby What is the JFLAP minimization doing that the other method is just missing. – Zimm3r Apr 2 '15 at 23:58