This paper addresses state minimization problems of different classes of non-deterministic finite state machines (NDFSMs). We present a theoretical solution to the problem of exact state minimization of general NDFSMs, based on the proposal of generalized compatibles. This gives an algorithmic frame to explore behaviors contained in a general NDFSM. Then we describe a fully implicit algorithm for state minimization of pseudo non-deterministic FSMs (PNDFSMs). The results of our implementation are reported and shown to be superior to a previous explicit formulation. We could solve exactly all but one problem of a published benchmark, while an explicit program could complete approximately one half of the examples, and in those cases with longer run times.