Single-Form Completeness of Expression

Accordingly, the notion of single-form completeness of expression is introduced; an expression that completely characterizes the behavior of a process in the context of a single conceptual form of expression eliminating the need for meta-coordination. A single-form complete expression will be sufficient unto itself and will behave autonomously with no need of external manipulation, control or interpretation. It will be the simplest and most direct form of expression embodying and revealing the essential nature of expression itself and of the process being expressed.

A single-form complete expression can also serve as a conceptual touchstone of comparison for other forms of expression. As expression deviates from a single-form completeness, introducing other forms that must be meta coordinated it is easier to relate the nature of each of the forms and the nature of their meta-coordination.

This paper investigates specifically the expression of combinational processes solely in terms of logical relationships. It will be shown that a combinational expression can be expressed completely in terms of logical relationships with a 4 value logic and that with logics of fewer values the logical completeness is compromised but that these compromises can be locally isolated within local logical relationships and their effect easily minimized. A practical 2 value logic is derived that retains sufficient logical expressivity to enable the practical possibility of logically determined system design.

If the behavior of a combinational process is completely logically determined, there need be no other form of expression such as temporal relationships. Consequently, the development of these ideas intersects strongly with the tradition of asynchronous circuit design. Delay insensitive is another way of saying logically determined. While the tradition of asynchronous design attempted to discover delay insensitivity in the context of insufficiently expressive Boolean Logic, [references: 5, 11, 12, 13] this paper discovers logics in the context of the sufficient expression of logical determination. Many of the concepts in the progression of development are familiar asynchronous design techniques. What is new here is the conceptual orientation of the quest, and the derivation rationale of the NULL Convention Logics [reference 2].

Can a combinational process be completely logically determined?

Can the behavior of a combinational process be completely expressed solely in terms of logical relationships? The first step is to logically determine the beginning and ending of a data set resolution.