The dependence on the initial states and the transitivity of the regular autonomous asynchronous systems

TL;DR

This paper explores how initial states influence the behavior of autonomous asynchronous systems and introduces the concept of transitivity, providing insights into their dynamical properties.

Contribution

It introduces the concepts of dependence on initial states and transitivity specifically for regular autonomous asynchronous systems, advancing understanding of their dynamical behavior.

Findings

Dependence on initial states affects system trajectories.

Transitivity is characterized for these systems.

Foundational concepts for analyzing asynchronous circuit models.

Abstract

The asynchronous systems are non-deterministic real time, binary valued models of the asynchronous circuits from electronics. Autonomy means that there is no input and regularity means analogies with the (real) dynamical systems. We introduce the concepts of dependence on the initial states and of transitivity for these systems.