Selected Topics in Asynchronous Automata

TL;DR

This paper explores the mathematical modeling of asynchronous automata, including delay types, stability, and logical connections, providing a comprehensive framework for understanding asynchronous circuit behavior.

Contribution

It introduces detailed equations for asynchronous automata combining various delay models and discusses their solutions and properties, advancing the theoretical understanding of asynchronous circuit models.

Findings

Solutions for automata equations in R->{0,1}

Analysis of stability and operation modes

Connections with temporal logic

Abstract

The paper is concerned with defining the electrical signals and their models. The delays are discussed, the asynchronous automata - which are the models of the asynchronous circuits - and the examples of the clock generator and of the R-S latch are given. We write the equations of the asynchronous automata, which combine the pure delay model and the inertial delay model; the simple gate model and the complex gate model; the fixed, bounded and unbounded delay model. We give the solutions of these equations, which are written on R->{0,1} functions, where R is the time set. The connection between the real time and the discrete time is discussed. The stability, the fundamental mode of operation, the combinational automata, the semi-modularity are defined and characterized. Some connections are suggested with the linear time and the branching time temporal logic of the propositions.