The decomposition of the regular asynchronous systems as parallel connection of regular asynchronous systems

TL;DR

This paper investigates conditions under which a regular asynchronous system can be decomposed into a parallel connection of simpler regular asynchronous systems, aiding understanding and design of complex asynchronous circuits.

Contribution

It provides theoretical conditions for decomposing regular asynchronous systems into parallel components, enhancing modular analysis of asynchronous circuits.

Findings

Decomposition conditions for regular asynchronous systems identified

Parallel connection of systems preserves regularity under certain conditions

Framework aids modular analysis of asynchronous circuit models

Abstract

The asynchronous systems are the non-deterministic models of the asynchronous circuits from the digital electrical engineering, where non-determinism is a consequence of the fact that modelling is made in the presence of unknown and variable parameters. Such a system is a multi-valued function f that assigns to an (admissible) input u:R{\to}{0,1}^{m} a set f(u) of (possible) states x:R{\to}{0,1}^{n}. When this assignment is defined by making use of a so-called generator function {\Phi}:{0,1}^{n}{\times}{0,1}^{m}{\to}{0,1}^{n}, then the asynchronous system f is called regular. The generator function {\Phi} acts in this asynchronous framework similarly with the next state function from a synchronous framework. The parallel connection of the asynchronous systems f' and f" is the asynchronous system (f'||f")(u)=f'(u){\times}f"(u). The purpose of the paper is to give the circumstances under which a regular asynchronous system f may be written as a parallel connection of regular asynchronous systems.