Publisher Summary This chapter discusses the state decompositions to explain state space approach. The advantage of such an approach is its extreme generality. It is also a rather down to earth (even “brute force”) approach. The universality of the state space approach is established by proving an existence theorem for state decompositions for T-processors. By addressing the constructive specifications based on state space paraphernalia, is the chapter shows how state equations arise in the theory. It also shows how state decompositions can be combined in interconnections, and one can obtain some results about the timeevolution of state decompositions. Finally, the existence of some special types of state decompositions for contracting, nonanticipatory T-processors is proved.