Weighing Obese Timed Languages

TL;DR

This paper introduces a method to compute the bandwidth of obese timed automata, which produce information at the maximal rate, by reducing the problem to a reward-to-time ratio in a weighted timed graph.

Contribution

It presents a novel approach to determine the bandwidth of obese timed automata using weighted timed graphs and entropy-based weights.

Findings

Bandwidth can be approximated as α/ε.

The method reduces bandwidth computation to reward-to-time ratio optimization.

Applicable to automata with unbounded event frequency.

Abstract

The bandwidth of a timed language characterizes the quantity of information per time unit (with a finite observation precision $\varepsilon$). Obese timed automata have an unbounded frequency of events and produce information at the maximal possible rate. In this article, we compute the bandwidth of any such automaton in the form $\approx\alpha/\varepsilon$. Our approach reduces the problem to computing the best reward-to-time ratio in a weighted timed graph constructed from the given timed automaton, with weights corresponding to the entropy of auxiliary finite automata.