Introduction to Formal Realizability Theory - I

2.0 Network theory provides direct means for associating with an electrical network a mathematical description which characterizes the behavior of that network. Typically, this results in shifting engineering attention from a detailed, possibly quite intricate, electrical structure to a mathematical entity which succinctly describes the relevant behavior of that structure. An essential feature of this shift in focus is emphasized by the word "relevant": only those terminals of the network which are directly relevant to the problem at hand are considered in the mathematical description. Design work can then be done in terms of constructs relating explicitly to these accessible terminals, the effect of the internal structure being felt only by implication. The physical origins of these mathematical constructs, and the implications of the internal structure upon them, cannot however be entirely forgotten, for they have mathematical consequences which are not always immediately evident. Until he knows these limitations-- imposed upon him by the physical nature or the necessary structural form of the networks he is designing--a design engineer cannot make free use of the mathematical tools that network theory has provided. We give the name "realizability theory" to that part of network theory which aims at the isolation and understanding of those broad limitations upon network performance, i.e., upon the mathematical constructs which describe that performance--which are imposed by limitations on the network structure.