Computing the Bandwidth of Meager Timed Automata

TL;DR

This paper introduces a method to compute the exact bandwidth of meager timed automata using a finite-state abstraction and polynomial root analysis, advancing understanding of information flow in timed systems.

Contribution

It presents a novel finite-state abstraction approach to precisely calculate the bandwidth of meager timed automata, extending previous qualitative classifications.

Findings

Bandwidth can be computed as the logarithm of the inverse of the smallest root of a characteristic polynomial.

The method provides an exact value for the bandwidth of meager automata.

The approach links automata structure to algebraic properties of polynomials.

Abstract

The bandwidth of timed automata characterizes the quantity of information produced/transmitted per time unit. We previously delimited 3 classes of TA according to the nature of their asymptotic bandwidth: meager, normal, and obese. In this paper, we propose a method, based on a finite-state simply-timed abstraction, to compute the actual value of the bandwidth of meager automata. The states of this abstraction correspond to barycenters of the faces of the simplices in the region automaton. Then the bandwidth is $\log 1/|z_0|$ where $z_0$ is the smallest root (in modulus) of the characteristic polynomial of this finite-state abstraction.