Functional Type Expressions of Sequential Circuits with the Notion of Referring Forms

TL;DR

This paper presents a novel theoretical framework using referring forms, based on type expressions, to analyze and understand the behavior of sequential circuits across multiple clock domains.

Contribution

It introduces the concept of referring forms as a new metric and identifies a universal property in multi-clock domain circuits, advancing the analysis of sequential circuits.

Findings

Referring forms effectively characterize circuit behavior.

Universal property identified in multi-clock domain circuits.

Framework enhances understanding of sequential circuit functions.

Abstract

This paper introduces the notion of referring forms as a new metric for analyzing sequential circuits from a functional perspective. Sequential circuits are modeled as causal stream functions, the outputs of which depend solely on the past and current inputs. Referring forms are defined based on the type expressions of functions and represent how a circuit refers to past inputs. The key contribution of this study is identifying a universal property in multiple clock domain circuits using referring forms. This theoretical framework is expected to enhance the comprehension and analysis of sequential circuits.