Hugo Rincon Galeana

ORCID

Papers together

2025

[C1]
Stephan Felber, Bernardo Hummes Flores and Hugo Rincon Galeana
Brief Announcement: A Sheaf-Theoretic Characterization of Tasks in Distributed Systems
SIROCCO 2025
DOI
abstract
Task solvability lies at the heart of distributed computing, with direct implications for both theoretical understanding and practical system design. A fundamental challenge in distributed computing is constructing global solutions from local computations and information. Sheaf theory addresses this challenge by providing a mathematical framework for assessing globally consistent properties from locally defined data. In this paper, we introduce a sheaf-theoretic characterization of task solvability by defining the novel construction of a task sheaf, whose sections correspond to valid solutions of a task. Furthermore, we show that the cohomology of a task sheaf may be used to compute solving protocols, thus establishing a connection between distributed computing and sheaf theory for both protocol design and impossibility analysis.
bibtex
```
@inproceedings{cignarale-felber-goubault-hummesflores-rincongaleana-2025,
  author = {Felber, Stephan and Hummes Flores, Bernardo and Rincon Galeana, Hugo},
  title = {Brief Announcement: A Sheaf-Theoretic Characterization of Tasks in Distributed Systems},
  isbn = {978-3-031-91735-6},
  publisher = {Springer-Verlag},
  address = {Berlin, Heidelberg},
  url = {https://doi.org/10.1007/978-3-031-91736-3_26},
  doi = {10.1007/978-3-031-91736-3_26},
  booktitle = {Structural Information and Communication Complexity: 32nd International Colloquium, SIROCCO 2025, Delphi, Greece, June 2–4, 2025, Proceedings},
  year = {2025},
  pages = {425–430},
  numpages = {6},
  location = {Delphi, Greece}
}
```
[P2]
Stephan Felber, Bernardo Hummes Flores and Hugo Rincon Galeana
A Sheaf-Theoretic Characterization of Tasks in Distributed Systems
arXiv preprint, 2025
arXiv
abstract
Task solvability lies at the heart of distributed computing, with direct implications for both theoretical understanding and practical system design. The field has evolved multiple theoretical frameworks for this purpose, including topological approaches, epistemic logic, and adversarial models, but these often address specific problem classes, limiting cross-domain applications. Our approach provides a unifying mathematical perspective across message-passing system models. We introduce a unifying sheaf-theoretic perspective that represents task solvability across message-passing system models while maintaining clear connections to the underlying distributed computing principles. A fundamental challenge in distributed computing is constructing global solutions from local computations and information. Sheaf theory addresses this challenge by providing a mathematical framework for assessing globally consistent properties from locally defined data, offering a natural language to describe and reason about distributed tasks. Sheaves have proven valuable in studying similar local-to-global phenomena, from opinion dynamics to contextuality in quantum mechanics and sensor integration. We now extend this framework to distributed systems. In this paper, we introduce a sheaf-theoretic characterization of task solvability in any model with a message based adversary. We provide a novel construction of a task sheaf, and prove that non-trivial sections correspond to valid solutions of a task, while obstructions to global sections represent system limitations that make tasks unsolvable. Furthermore, we also show that the cohomology of a task sheaf may be used to compute solving protocols. This opens space for new connections between distributed computing and sheaf theory for both protocol design and impossibility analysis.
bibtex
```
@unpublished{cignarale-felber-goubault-hummesflores-rincongaleana-2025,
  author = {Felber, Stephan and Hummes Flores, Bernardo and Rincon Galeana, Hugo},
  year = {2025},
  month = march,
  doi = {10.48550/arXiv.2503.02556},
  eprint = {2503.02556},
  eprintclass = {cs.DC},
  eprinttype = {arXiv},
  note = {Unpublished manuscript},
  title = {A Sheaf-Theoretic Characterization of Tasks in Distributed Systems},
}
```
[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},
}
```