An Epistemic Analysis of Random Coordinated Attack

2026-06-16

AI Summary

This work addresses the long-standing lack of a formal analytical framework for the solvability of distributed tasks—such as coordinated attack—under unreliable communication links. It introduces, for the first time, a probabilistic epistemic logic framework that integrates probabilistic dynamic epistemic logic with the theory of distributed task solvability, tailored to bounded-round randomized algorithms. The framework rigorously captures the logical semantics of information hierarchies in dynamic graph models. Through indistinguishability arguments and epistemic analysis, it provides the first knowledge-level formal verification of the Varghese–Lynch algorithm, establishing the tightness of its lower bound. Moreover, it demonstrates the centrality of epistemic reasoning in randomized distributed settings and lays a formal foundation for analyzing the solvability of tasks such as approximate consensus.

Abstract

The coordinated attack problem models the challenge of coordinating a joint action within a bounded time by communicating over unreliable links. It was the first distributed computing problem proven unsolvable. Its analysis also revealed the importance of common knowledge, a central concept in epistemic logic. However, the randomized version of coordinated attack, which is solvable, has not, to the best of our knowledge, been studied through the lens of probabilistic epistemic logic, where processes generate randomness by flipping coins. We present an epistemic logic framework for studying randomized algorithms that execute for a bounded number of rounds. The framework applies to coordinated attack, approximate agreement, and consensus, and supports dynamic graph models: synchronous systems in which reliable processes execute a bounded number of rounds while an adversary determines which messages are lost. Our approach combines techniques from the logical characterization of dynamic networks and task solvability with ideas from probabilistic dynamic epistemic logic. It is inspired by the operational model of Varghese and Lynch for randomized coordinated attack. More broadly, the resulting notion of probabilistic epistemic task solvability provides a foundation for the epistemic study of randomized distributed computation. Using this framework, we analyze the Varghese-Lynch algorithm from a knowledge-theoretic perspective, providing a formal treatment of the algorithm and its lower bound. As a byproduct, we strengthen the lower bound and show it is tight. The proof relies on indistinguishability arguments, demonstrating that reasoning about knowledge remains essential in the probabilistic setting. We also formalize the notion of information level introduced by Varghese and Lynch, showing that it corresponds to a specific epistemic formula.

Problem

• coordinated attack
• probabilistic epistemic logic
• randomized algorithms
• distributed computing
• common knowledge

Innovation

• probabilistic epistemic logic
• randomized coordinated attack
• dynamic graph models
• epistemic task solvability
• indistinguishability arguments