Éric Goubault

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Professor of computer science in École Polytechnique.

Papers together

2025

[P3]
Éric Goubault, Bernardo Hummes Flores, Roman Kniazev, Jérémy Ledent and Sergio Rajsbaum
A categorical and logical framework for iterated protocols
arXiv preprint, 2025
arXiv
abstract
In this article, we show that the now classical protocol complex approach to distributed task solvability of Herlihy et al. can be understood in standard categorical terms. First, protocol complexes are functors, from chromatic (semi-) simplicial sets to chromatic simplicial sets, that naturally give rise to algebras. These algebras describe the next state operator for the corresponding distributed systems. This is constructed for semi-synchronous distributed systems with general patterns of communication for which we show that these functors are always Yoneda extensions of simpler functors, implying a number of interesting properties. Furthermore, for these protocol complex functors, we prove the existence of a free algebra on any initial chromatic simplicial complex, modeling iterated protocol complexes. Under this categorical formalization, protocol complexes are seen as transition systems, where states are structured as chromatic simplicial sets. We exploit the epistemic interpretation of chromatic simplicial sets and the underlying transition system (or algebra) structure to introduce a temporal-epistemic logic and its semantics on all free algebras on chromatic simplicial sets. We end up by giving hints on how to extend this framework to more general dynamic network graphs and state-dependent protocols, and give example in fault-tolerant distributed systems and mobile robotics.
bibtex
```
@unpublished{goubault-hummesflores-kniazev-ledent-rajsbaum-2025,
  author = {Goubault, Eric and Hummes Flores, Bernardo and Kniazev, Roman and Ledent, Jeremy and Rajsbaum, Sergio},
  year = {2025},
  month = may,
  doi = {10.48550/arXiv.2505.10071},
  eprint = {2505.10071},
  eprintclass = {cs.LO},
  eprinttype = {arXiv},
  note = {Unpublished manuscript},
  title = {A categorical and logical framework for iterated protocols},
}
```
[P1]
Stephan Felber, Giorgio Cignarale, Éric Goubault, Bernardo Hummes Flores and Hugo Rincon Galeana
Knowledge in multi-robot systems: an interplay of dynamics, computation and communication
arXiv preprint, 2025
arXiv
abstract
We show that the hybrid systems perspective of distributed multi-robot systems is compatible with logical models of knowledge already used in distributed computing, and demonstrate its usefulness by deriving sufficient epistemic conditions for exploration and gathering robot tasks to be solvable. We provide a separation of the physical and computational aspects of a robotic system, allowing us to decouple the problems related to each and directly use methods from control theory and distributed computing, fields that are traditionally distant in the literature. Finally, we demonstrate a novel approach for reasoning about the knowledge in multi-robot systems through a principled method of converting a switched hybrid dynamical system into a temporal-epistemic logic model, passing through an abstract state machine representation. This creates space for methods and results to be exchanged across the fields of control theory, distributed computing and temporal-epistemic logic, while reasoning about multi-robot systems.
bibtex
```
@unpublished{cignarale-felber-goubault-hummesflores-rincongaleana-2025,
  author = {Cignarale, Giorgio and Felber, Stephan and Goubault, Eric and Hummes Flores, Bernardo and Rincon Galeana, Hugo},
  year = {2025},
  month = january,
  doi = {10.48550/arXiv.2501.18309},
  eprint = {2501.18309},
  eprintclass = {cs.LO},
  eprinttype = {arXiv},
  note = {Unpublished manuscript},
  title = {Knowledge in multi-robot systems: an interplay of dynamics, computation and communication},
}
```