Representation of Sequential Circuits in Combinatory Logic

1.1 We will be dealing with "sequential circuits" in the sense of E. F. Moore' and G. H. Mealy.2 Each such circuit is assumed to have a finite number of input wires (possibly none) and a finite number of output wires (but at least one). Each element of such a circuit will be assumed to be an and-circuit, an or-circuit, a not-circuit, or a delay circuit, for some specified temporal delay. Each element has one output wire which, however, may branch in order to serve several purposes simultaneously. (Similarly the inputs of the total circuit may be allowed to branch.) The and-circuits and or-circuits have two input wires each, while the not-circuits and the delay circuits have one input wire each. 1.2 In constructing a sequential circuit, each input of an element and each output of the total circuit, must be either an input of the total circuit (or a branch of one such input) or an output of some element of the circuit (or a branch of one such output). Here is an example of such a sequential circuit: