A simplicial complex model for dynamic epistemic logic to study distributed task computability

Éric Goubault, Jérémy Ledent, Sergio Rajsbaum

Research output: Contribution to journalArticle

Abstract

The usual S5 n epistemic model for a multi-agent system is based on a Kripke frame, which is a graph whose edges are labeled with agents that do not distinguish between two states. We propose to uncover the higher dimensional information implicit in this structure, by considering a dual, simplicial complex model. We use dynamic epistemic logic (DEL) to study how an epistemic simplicial complex model changes after a set of agents communicate with each other. We concentrate on an action model that represents the so-called immediate snapshot communication patterns of asynchronous agents, because it is central to distributed computability (but our setting works for other communication patterns). There are topological invariants preserved from the initial epistemic complex to the one after the action model is applied, which determine the knowledge that the agents gain after communication. Finally, we describe how a distributed task specification can be modeled as a DEL action model, and show that the topological invariants determine whether the task is solvable. We thus provide a bridge between DEL and the topological theory of distributed computability, which studies task solvability in a shared memory or message passing architecture.

Original languageEnglish
Article number104597
JournalInformation and Computation
Early online date11 Jun 2020
DOIs
Publication statusE-pub ahead of print - 11 Jun 2020

Keywords

  • simplicial complexes
  • epistemic logic
  • distributed computing

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