Monitoring Diameters of Causal Communication Graph with Spatio-Temporal Logic

2026-06-19

AI Summary

This work addresses the limitations of existing logics in expressing distance-constrained reachability and communication link length in multi-agent systems, which hinder decentralized monitoring and analysis of communication graph diameter. By extending the muTGL spatio-temporal logic with a spatial horizon operator, the proposed framework is the first to support modalities such as distance-bounded reachability and escape, thereby enhancing expressiveness for spatio-temporally coupled properties. Building on this logic, the authors devise a centralized offline monitoring algorithm that integrates graph-theoretic and formal verification techniques to effectively analyze the diameter of causal communication graphs. The approach is successfully applied to simulation-based verification of distributed task allocation protocols, such as the Consensus-Based Bundle Algorithm, accurately capturing dynamic changes in communication topology and its diameter.

Abstract

Verification of multi-agent systems requires the ability to check meticulous topological properties when it comes to agents that can move through space in continuous time. This demands a logic with sufficient expressiveness to capture these dynamics. MuTGL logic has interesting properties for expressing entangled space-time properties. However, this logic lacks the expressivity needed to analyse reachability within specific distance bounds, or to track the length or the cost of communication chains: these are fundamental for decentralized monitoring, or graph-theoretic analysis of distributed protocols, where algorithmic complexities often relates with the system's communication graph diameter. We then introduce an extension of muTGL, including a new operator called the space horizon. This addition allows us to bound the distance of communication chains, hence enhancing the logic's expressiveness. We show that this operator allows to encode modalities from other logics, such as reachability or escaping which were not available in vanilla muTGL, while allowing a deeper entanglement of spatial and temporal properties. We provide a centralized offline monitoring algorithm for this logic and illustrate it on several examples on simulations of Consensus-Based Bundle Algorithms, distributed protocols for task allocation.

Problem

• multi-agent systems
• spatio-temporal logic
• communication graph diameter
• reachability
• decentralized monitoring

Innovation

• space horizon
• muTGL logic
• spatio-temporal logic
• communication graph diameter
• multi-agent monitoring