State Minimization Using am Implication Table: Summary of Approach
?? Construct an implication table which contains a square for each pair of states. Label each row q2, q3, ... qn and column q1, q2, qn-1 (no need for diagonal).
?? Compare each each pair of rows in the state table. If the outputs associated with states i and j are different, put an ???in square i-j to indicate that i ??j (trivial non-equivalence). If the outputs and the next states are the same, put a ??in square i-j to indicate i ??j (trivial equivalence).
?? In all other squares, put state-pairs that must be equivalent if states i-j are to be equivalent (if the next states of i and j are m and n for some input ??, then m-n is an implied pair and goes in square i-j).
?? Go through the non- ??and?non- ???squares, one at a time. If square i-j contains an implied pair and square m-n contains an ??, then i ??j so put an ?? in i-j as well.
? If any ??'s were added in the last step, repeat it until no more ??'s are added. For each square i-j which not containing an ??, i ??j.