View source for NFA to DFA ← NFA to DFA

[http://condor.depaul.edu/glancast/444class/docs/nfa2dfa.html Conversion]

*'''Q:''' I know that $2^n$ are the maximum states in DFA for an $n$  state NFA. But what about the minimum no of states in a DFA for an $n$ state NFA?

A: I would say 1 because the $n$ states can be connected through $ε$ moves and hence all of these will be combines to a single start state in DFA. 

*'''Q:''' After converting from  NFA to DFA and  we get $2^n$ states. Now we apply minimization- how many states can we get after this? 
A: In the worst case this can remain $2^n$ - that is no minimization can be possible. We can see this in the following example 
===NFA===
<graphviz caption='NFA'>
digraph NFA {
rankdir=LR;
node [shape = none] "";
node [shape = doublecircle] q2;
node [shape = circle];

""-> q1;
q1->q2 [label="a"];
q1->q2 [label="a"];
q2 -> q2 [label="b"];
}
</graphviz>

===DFA===
<graphviz caption='DFA'>
digraph DFA {
rankdir=LR;
node [shape = none] "";
node [shape = doublecircle] q2, q12;
node [shape = circle];

""-> q1;
q1->q12 [label="a"];
q12->q12 [label="a"];
q12->q2 [label="b"];
q2->q2 [label="b"];
q2 -> q3 [label="a"];
q1 -> q3 [label="b"];
}
</graphviz>