Descriptive Complexity for Distributed Computing with Circuits

Authors Veeti Ahvonen , Damian Heiman , Lauri Hella , Antti Kuusisto



PDF
Thumbnail PDF

File

LIPIcs.MFCS.2023.9.pdf
  • Filesize: 0.74 MB
  • 15 pages

Document Identifiers

Author Details

Veeti Ahvonen
  • Tampere University, Finland
Damian Heiman
  • Tampere University, Finland
Lauri Hella
  • Tampere University, Finland
Antti Kuusisto
  • Tampere University, Finland
  • University of Helsinki, Finland

Cite As Get BibTex

Veeti Ahvonen, Damian Heiman, Lauri Hella, and Antti Kuusisto. Descriptive Complexity for Distributed Computing with Circuits. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 9:1-9:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.MFCS.2023.9

Abstract

We consider distributed algorithms in the realistic scenario where distributed message passing is operated by circuits. We show that within this setting, modal substitution calculus MSC precisely captures the expressive power of circuits. The result is established via constructing translations that are highly efficient in relation to size. We also observe that the coloring algorithm based on Cole-Vishkin can be specified by logarithmic size programs (and thus also logarithmic size circuits) in the bounded-degree scenario.

Subject Classification

ACM Subject Classification
  • Theory of computation → Finite Model Theory
  • Theory of computation → Distributed algorithms
  • Networks → Network algorithms
  • Theory of computation → Modal and temporal logics
Keywords
  • Descriptive complexity
  • distributed computing
  • logic
  • graph coloring

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. Veeti Ahvonen, Damian Heiman, Lauri Hella, and Antti Kuusisto. Descriptive complexity for distributed computing with circuits. CoRR, abs/2303.04735v1, 2023. URL: https://doi.org/10.48550/arXiv.2303.04735.
  2. Pablo Barceló, Egor V. Kostylev, Mikaël Monet, Jorge Pérez, Juan L. Reutter, and Juan Pablo Silva. The logical expressiveness of graph neural networks. In 8th International Conference on Learning Representations, ICLR 2020. OpenReview.net, 2020. Google Scholar
  3. Leonid Barenboim and Michael Elkin. Distributed graph coloring. Synthesis Lectures on Distributed Computing Theory, 11, 2013. Google Scholar
  4. Benedikt Bollig, Patricia Bouyer, and Fabian Reiter. Identifiers in registers - Describing network algorithms with logic. CoRR, abs/1811.08197, 2018. Google Scholar
  5. Richard Cole and Uzi Vishkin. Deterministic coin tossing with applications to optimal parallel list ranking. Information and Control, 70(1):32-53, 1986. Google Scholar
  6. Andrew Goldberg, Serge Plotkin, and Gregory Shannon. Parallel symmetry-breaking in sparse graphs. Proceedings of the nineteenth annual ACM symposium on Theory of computing, pages 315-324, 1987. Google Scholar
  7. Martin Grohe. The logic of graph neural networks. In 36th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2021, pages 1-17. IEEE, 2021. Google Scholar
  8. Lauri Hella, Matti Järvisalo, Antti Kuusisto, Juhana Laurinharju, Tuomo Lempiäinen, Kerkko Luosto, Jukka Suomela, and Jonni Virtema. Weak models of distributed computing, with connections to modal logic. In Darek Kowalski and Alessandro Panconesi, editors, ACM Symposium on Principles of Distributed Computing, PODC '12, pages 185-194. ACM, 2012. Google Scholar
  9. Lauri Hella, Matti Järvisalo, Antti Kuusisto, Juhana Laurinharju, Tuomo Lempiäinen, Kerkko Luosto, Jukka Suomela, and Jonni Virtema. Weak models of distributed computing, with connections to modal logic. Distributed Comput., 28(1):31-53, 2015. Google Scholar
  10. Stefanie Jegelka. Theory of graph neural networks: Representation and learning. arXiv preprint, 2022. URL: https://arxiv.org/abs/2204.07697.
  11. Antti Kuusisto. Modal Logic and Distributed Message Passing Automata. In Computer Science Logic 2013 (CSL 2013), volume 23 of Leibniz International Proceedings in Informatics (LIPIcs), pages 452-468, 2013. Google Scholar
  12. Tuomo Lempiäinen. Logic and Complexity in Distributed Computing. PhD thesis, Aalto University, 2019. Google Scholar
  13. Leonid Libkin. Elements of Finite Model Theory. Texts in Theoretical Computer Science. An EATCS Series. Springer, 2004. Google Scholar
  14. Andreas Loukas. What graph neural networks cannot learn: depth vs width. arXiv preprint, 2019. URL: https://arxiv.org/abs/1907.03199.
  15. Fabian Reiter. Asynchronous distributed automata: A characterization of the modal mu-fragment. In I. Chatzigiannakis, P. Indyk, F. Kuhn, and A. Muscholl, editors, 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017, volume 80 of LIPIcs, pages 100:1-100:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. Google Scholar
  16. Fabian Reiter. Distributed Automata and Logic. (Automates Distribués et Logique). PhD thesis, Sorbonne Paris Cité, France, 2017. Google Scholar
  17. Ryoma Sato, Makoto Yamada, and Hisashi Kashima. Random features strengthen graph neural networks. In Proceedings of the 2021 SIAM International Conference on Data Mining (SDM), pages 333-341. SIAM, 2021. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail