The consistency, the composition and the causality of the asynchronous flows

TL;DR

This paper investigates asynchronous flows derived from digital circuits, demonstrating they satisfy key properties like consistency, composition, and causality, thereby aligning with dynamical systems theory.

Contribution

It establishes that asynchronous flows from digital circuits adhere to fundamental dynamical system properties, bridging electrical engineering models with mathematical dynamical systems.

Findings

Asynchronous flows satisfy consistency, composition, and causality.

They behave as dynamical systems with well-defined properties.

The results connect digital circuit models with theoretical dynamical systems.

Abstract

Let $\Phi:\{0,1\}^{n}\longrightarrow\{0,1\}^{n}$. The asynchronous flows are (discrete time and real time) functions that result by iterating the coordinates $\Phi_{i}$ independently on each other. The purpose of the paper is that of showing that the asynchronous flows fulfill the properties of consistency, composition and causality that define the dynamical systems. The origin of the problem consists in modelling the asynchronous circuits from the digital electrical engineering.