DFA minimize

epsilon transition in NDF is a problem and remove it is important step before convert to DFA therefore to remove epsilon transition we determined subset which can arrival with epsilon transition and select final states due to union between these subset and original final set.
in DFA minimize we appear the concept of relation between pair of states if one of pair is belong to final set this called distinct other is called indistinct(we mean by other is both not belong to final set or both belong to final set).
Start with an automaton A without unreachable states. If A has distinguishable states p; q, combine them into one state. (For instance, remove q and reroute all transitions into q to go into p instead.) Repeat this process until no more distinguishable states can be found. At this point we will not be able to reduce A further. But does it necessarily mean that A is minimum? Conceivably, there could be a completely dierent automaton B, with a completely dierent topology but with fewer states, that accepts the same language as A. Quite remarkably, it turns out that
this is impossible, namely, any automaton whose all states are pairwise distinguishable must be minimum