Monitorability for the Modal mu-Calculus over Systems with Data: From Practice to Theory

2025-06-06

AI Summary

This work addresses runtime monitoring of modal μ-calculus over infinite-domain data systems, focusing on specification and verification of data-flow properties. Methodologically, it introduces a data-enriched modal μ-calculus, integrating first-order predicates, register automata with guessing capabilities, and monitor synthesis algorithms. The study establishes the first rigorous monitorability hierarchy for this logic; proves that deterministic monitors strictly reduce expressive power; identifies the fragment without greatest fixed points as precisely characterizing all monitorable formulas; and shows that no decidable and complete monitorable sublogic exists for the full logic. Contributions include: (i) a formal characterization of the theoretical limits of data-aware monitoring, (ii) the undecidability of completeness for monitorability in data logics, and (iii) a framework for monitor construction that balances theoretical soundness with engineering feasibility.

Technology Category

• Knowledge Representation and Reasoning: Nonmonotonic Reasoning
• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Security and Privacy: Data transparency and provenance

Abstract

Runtime verification, also known as runtime monitoring, consists of checking whether a system satisfies a given specification by observing the trace it produces during its execution. It is used as a lightweight verification technique to complement or substitute costlier methods such as model-checking. In the regular setting, Hennessy-Milner logic with recursion, a variant of the modal mu-calculus, provides a versatile formalism for expressing linear- and branching-time specifications of the control flow of the system. In this paper, we shift the focus from control to data and study the monitorability of an extension of this logic that allows one to express properties of the data flow. Data values are modelled as values from an infinite domain. They are stored using data variables and manipulated using predicates and first-order quantification. The resulting logic is closely related to register automata with guessing. This correspondence yields a monitor synthesis algorithm, and allows us to derive a strict monitorability hierarchy between the different fragments of the logic, in stark contrast to the regular setting. In particular, restricting to deterministic monitors strictly reduces the set of monitorable properties. Last, we exhibit a fragment of the logic that can express all monitorable formulae in the logic without greatest fixed-points but not in the full logic. We finally show that this is unavoidable because, in fact, there is no decidable fragment of the logic that captures all monitorable properties.

Problem

• Extends modal mu-calculus to monitor data flow properties
• Studies monitorability hierarchy in logic with infinite data domains
• Identifies undecidability of capturing all monitorable properties

Innovation

• Extends modal mu-calculus with data flow properties
• Uses register automata with guessing for synthesis
• Identifies strict monitorability hierarchy for logic fragments