Bernardo Hummes Flores

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.

@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}
}

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.

@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},
}

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.

@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},
}

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.

@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},
}

A reliable quantification of the worst-case influence of model uncertainty and external disturbances is crucial for the localization of vessels in marine applications. This is especially true if uncertain GPS-based position measurements are used to update predicted vessel locations that are obtained from the evaluation of a ship’s state equation. To reflect real-life working conditions, these state equations need to account for uncertainty in the system model, such as imperfect actuation and external disturbances due to effects such as wind and currents. As an application scenario, the GPS-based localization of autonomous DDboat robots is considered in this paper. Using experimental data, the efficiency of an ellipsoidal approach, which exploits a bounded-error representation of disturbances and uncertainties, is demonstrated.

@article{rauh-gourret-lagattu-hummes-jaulin-reuter-wirtensohn-hoher-2022.,
  title = {Experimental Validation of Ellipsoidal Techniques for State Estimation in Marine Applications},
  author = {Rauh, Andreas and Gourret, Yohann and Lagattu, Katell and Hummes, Bernardo and Jaulin, Luc and Reuter, Johannes and Wirtensohn, Stefan and Hoher, Patrick}},
  year = {2022},
  journal = {Algorithms},
  volume = {15},
  number = {5},
  article-number = {162},
}

For a mobile robot to operate in its environment it is crucial to determine its position with respect to an external reference frame using noisy sensor readings. A scenario in which the robot is moved to another position during its operation without being told, known as the kidnapped robot problem, complicates global localisation. In addition to that, sensor malfunction and external influences of the environment can cause unexpected errors, called outliers, that negatively affect the localisation process. This paper proposes a method based on the fusion of a particle filter with bounded-error localisation, which is able to deal with outliers in the measurement data. The application of our algorithm to solve the kidnapped robot problem using simulated data shows an improvement over conventional probabilistic filtering methods.

@article{neuland-mantelli-hummes-jaulin-maffei-prestes-kolberg-2021,
  title = {Robust Hybrid Interval-Probabilistic Approach for the Kidnapped Robot Problem},
  author = {Neuland, Renata and Mantelli, Mathias and Hummes, Bernardo and Jaulin, Luc and Maffei, Renan and Prestes, Edson and Kolberg, Mariana},
  year = {2021},
  journal = {International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems},
  volume = {29},
  number = {02},
  pages = {313-331},
  month = february,
}