A Minimization Algorithm :
We now produce an algorithm to construct the minimal state DFA from any given DFA accepting L by merging states inductively.
The algorithm assume that all states are reachable from the start state i.e. there is no inaccessible states. The algorithm keeps on marking pairs of states ( p, q ) as soon as it determines that p and q are distinguishable i.e. 
. The pairs are, of course, unordered i.e. pairs ( p, q ) and ( q , p) are considered to be identical. The steps of the algorithm are given below.
- For every p, q
Q , initially unmark all pairs ( p, q ). - If
and 
(or vice versa ) then mark ( p, q ). - Repeat the following step until no more changes occur : If there exists an unmarked pair ( p, q ) such that
is marked for some 
, then mark ( p, q ). 
iff ( p, q ) is unmarked.
The algorithm correctly computes all pairs of states that can be distingusihed i.e. unmarked.