Theory of Logical Nets

The aim of this paper is to place on a more rigorous basis the application of two-valued logic to digital computing circuits. To this end we study the formal properties of various logical nets some of which represent such circuits to a useful degree. A logical net is an array constructed from two primitive elements: a "stroke element," by means of which circuit components performing logical functions may be represented, and a "delay element," used in the representation of memory components. With each net is associated a set of equations useful in studying the behavior of that net. Various types of nets (well-behaved, deterministic, well-formed) are precisely defined and properties of each type are correlated with properties of the associated sets of equations. The relations between the various types of nets are investigated and some study is made of the kinds of operations performed by each. Finally, the question: "To what class of nets do digital computer circuits correspond?" is discussed.