Equivalence Relations
Equivalence relation: let R be a relation on a set S. R is an equivalence relation on S if and only if it is reflexive, symmetric, and transitive. An equivalence relation on a set partitions the set into disjoint equivalence classes.
Example: let S = {A,B,C,D,E,F,G,H} and R = {(A,A),(B,B),(B,H),(C,C),(D,D),(D,E),(E,E),(E,D),(F,F),(G,G),(H,H),
(H,B)}. Then P = (A)(BH)(C)(DE)(F)(G)
Theorem: state equivalence in a sequential circuit is an equivalence relation on the set of states.
Theorem: the equivalence classes defined by the state equivalence of a sequential circuit can be used as the states in an equivalent circuit.