# Finite Automata

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After  minimzing, only 4 states left then why 6 ?

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i'm getting [q0,q3,q4],[q5],[q1,q2] as 3 states plz verify it, how set [q0,q3,q4]  will partition into 2 groups??

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yes there are four states but in the question he is asking the different sets not the states so after minimization six different sets would be there & they are :

{{q3},{q5}{q1,q2},{q0,q4}{q0,q3,q4},{0,3,4,5}}

read the question carefully.
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i'm just asking for MDFA containing how many states??
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@Raghav Khajuria
@manisha11

Yeah, thanks.
I got confused when I read Myhill- Nerode because then i thought of equivalence class.

What would be the answer if they ask for equivalence classes for given FA.
Will it be 4 as its MDFA has 4 states ?

Or, Myhill - Nerode itselt is applied on MDFA only ?
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@Hira Thakur

4 states. Look in the given solution. The already applied minimisation.

$q_3$ has a separate partition as $q_3$ on $a$ is going to $q_5$ which is a different partition hence $q_3$ is not equivalent to $q_0$ and $q_4$.

1 vote
In the question, they aren't asking about the number of minimal states but they are asking distinct sets, that were observed in the minimization process.So it is 6.

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