Technology Category
Machine Learning: Information TheoryPlanning, Routing, and Scheduling: Optimization of Spatio-temporal SystemsNatural Language Processing: Information Extraction
Weighing Obese Timed Languages
🤖 AI Summary
This paper investigates the information bandwidth—i.e., the maximum information production rate per unit time—of languages generated by obese timed automata. To address this problem, we propose the first computable method for exact bandwidth estimation: we construct a weighted timed graph model, formulate bandwidth as an optimal reward-to-time ratio problem, and introduce an entropy-weighting mechanism alongside an asymptotic analysis framework under finite observation precision ε. By integrating timed automata theory, finite-state entropy quantification, and optimal path analysis, we derive, for the first time, a closed-form bandwidth expression ≈ α/ε, where α depends solely on the system’s structural parameters and event frequencies. This result provides a theoretical characterization of the ultimate information-rate limit for high-frequency event systems, overcoming the longstanding limitation in timed-language information theory: the absence of quantitative bandwidth analysis.
Technology Category
Application Category
📝 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 $approxα/varepsilon$. 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.
Problem
Research questions and friction points this paper is trying to address.
Computing bandwidth of obese timed automata
Reducing bandwidth calculation to reward-time ratio
Deriving information rate from weighted timed graphs
Innovation
Methods, ideas, or system contributions that make the work stand out.
Computing bandwidth via reward-time ratio
Constructing weighted timed graphs
Using entropy weights from automata
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