Universal regular autonomous asynchronous systems: omega-limit sets, invariance and basins of attraction

TL;DR

This paper extends dynamical systems concepts like omega-limit sets, invariance, and basins of attraction to universal regular autonomous asynchronous systems, which model non-deterministic asynchronous circuits without inputs.

Contribution

It introduces a framework for analyzing asynchronous circuit models using dynamical systems theory, defining key concepts like omega-limit sets and basins of attraction in this context.

Findings

Defined omega-limit sets for asynchronous systems

Established invariance properties in the model

Characterized basins of attraction for the systems

Abstract

The asynchronous systems are the non-deterministic real time-binary models of the asynchronous circuits from electrical engineering. Autonomy means that the circuits and their models have no input. Regularity means analogies with the dynamical systems, thus such systems may be considered to be the real time dynamical systems with a 'vector field' {\Phi}:{0,1}^2 \rightarrow {0,1}^2. Universality refers to the case when the state space of the system is the greatest possible in the sense of the inclusion. The purpose of the paper is that of defining, by analogy with the dynamical systems theory, the {\omega}-limit sets, the invariance and the basins of attraction of the universal regular autonomous asynchronous systems.