Binary signals: a note on the prime period of a point

TL;DR

This paper investigates the periodicity of signals in asynchronous systems, focusing on the existence of prime periods for points in the signals' orbits, contributing to the understanding of their fundamental properties.

Contribution

It provides a theoretical note on the conditions for the existence of prime periods in signals within asynchronous systems.

Findings

Characterization of periodic points in signals

Conditions for the existence of prime periods

Insights into asynchronous system behavior

Abstract

The 'nice' $x:\mathbf{R}\rightarrow\{0,1\}^{n}$ functions from the asynchronous systems theory are called signals. The periodicity of a point of the orbit of the signal x is defined and we give a note on the existence of the prime period.