Some properties of the regular asynchronous systems

TL;DR

This paper explores properties of regular asynchronous systems, which model digital circuits, focusing on their generation via generator functions and extending previous research in this area.

Contribution

It advances the understanding of regular asynchronous systems by analyzing their properties and the role of generator functions in their structure.

Findings

Characterization of regular asynchronous systems

Properties of generator functions in system generation

Extension of previous theoretical frameworks

Abstract

The asynchronous systems are the models of the asynchronous circuits from the digital electrical engineering. An asynchronous system f is a multi-valued function that assigns to each admissible input u a set f(u) of possible states x in f(u). A special case of asynchronous system consists in the existence of a Boolean function \Upsilon such that for any u and any x in f(u), a certain equation involving \Upsilon is fulfilled. Then \Upsilon is called the generator function of f (Moisil used the terminology of network function) and we say that f is generated by \Upsilon. The systems that have a generator function are called regular. Our purpose is to continue the study of the generation of the asynchronous systems that was started in [2], [3].