we now going to devise an algorithm for doing this until no more merging is possible. we start with the following observations.

• It is not possible to merge an accept state p and a non-accepting state q. Because if and for some , then x must be accepted and y must be rejected after merging p and q. But, now, the resulting merged state can neither be considered as an accept state nor as a non-accepting one.
• If p and q are merged, then we need to merge and , for every , as well, to maintain determinism.