State Minimization of Completely-Specified Machines
? Two states are said to be k-equivalent if, when excited by an input sequence of k symbols, yield identical output sequences. The machine can be partitioned by this k-equivalence relation into k-equivalence classes.
? For any n-state machine, there can be at most (n-1) successive, distinct partitions.
? For any n-state machine, these equivalence classes contain one and only one unique state.
? To minimize a completely-specified machine:
(1) Find the 1-equivalence classes, 2-equivalence classes, etc. until the k+1 equivalence classes are the same as the K equivalence classes, then stop.
(2) Combine all the states in the same class into a single state. If the machine has m equivalence classes, the machine has m states.