Omega-Regular Robustness

2025-03-16

AI Summary

This paper addresses the challenge of quantitatively comparing system robustness under ω-regular specifications. We propose a semantic-driven, syntax-independent robustness preference relation grounded in ω-automaton semantics and partial-order modeling. Unlike prior approaches, it enables decidable, qualitative robustness ranking within formal specification frameworks—without reliance on syntactic representations. Our contributions are threefold: (1) a formal definition of the “more robust” relation between systems satisfying the same ω-regular specification, jointly capturing response timeliness and behavioral stability; (2) rigorous adherence to natural rationality axioms ensuring intuitive and consistent ordering; and (3) a decidable verification framework that supports exact, comparative robustness analysis across distinct implementations. This work fills a fundamental gap in formal robustness theory by establishing the first sound, complete, and algorithmically verifiable foundation for robustness comparison under ω-regular properties.

Technology Category

• Natural Language Processing: Safety and Robustness
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Philosophy and Ethics of AI: Safety, Robustness & Trustworthiness

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Roughly speaking, a system is said to be robust if it can resist disturbances and still function correctly. For instance, if the requirement is that the temperature remains in an allowed range $[l,h]$, then a system that remains in a range $[l',h']subset[l,h]$ is more robust than one that reaches $l$ and $h$ from time to time. In this example the initial specification is quantitative in nature, this is not the case in $omega$-regular properties. Still, it seems there is a natural robustness preference relation induced by an $omega$-regular property. E.g. for a property requiring that every request is eventually granted, one would say that a system where requests are granted two ticks after they are issued is more robust than one in which requests are answered ninety ticks after they are issued. In this work we manage to distill a robustness preference relation that is induced by a given $omega$-regular language. The relation is a semantic notion (agnostic to the given representation of $L$) that satisfies some natural criteria.

Problem

• Defines robustness for systems under ω-regular properties.
• Establishes a robustness preference relation for ω-regular languages.
• Proposes a semantic notion of robustness independent of language representation.

Innovation

• Defines robustness via ω-regular properties
• Introduces semantic robustness preference relation
• Applies to systems with ω-regular language specifications