Classification of Sequential Circuits as Causal Functions

Abstract

In sequential circuits, the current output can depend on both past and current inputs. However, certain kinds of sequential circuits do not refer to all of the past inputs to generate the current output; but only to a subset of past inputs. This paper investigates which subset of past inputs a sequential circuit refers to, and proposes a new classification of sequential circuits based on this criterion. While the conventional classification of sequential circuits distinguishes between synchronous and asynchronous circuits, the new classification consolidates synchronous circuits and multiple clock domain circuits into the same category. This is consistent with the notion that “multiple clock domain circuits are analogous to synchronous circuits,” and thus, the proposed classification appears valid from this perspective. It is expected that a method underlying our classification will allow a deeper understanding of sequential circuits.