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Descriptive Complexity for Distributed Computing with Circuits

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

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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

Funding

Antti Kuusisto and Veeti Ahvonen were supported by the Academy of Finland project Theory of computational logics, grant numbers 352419, 352420, 353027, 324435, 328987. Antti Kuusisto was also supported by the Academy of Finland consortium project Explaining AI via Logic (XAILOG), grant number 345612. Veeti Ahvonen was also supported by the Vilho, Yrjö and Kalle Väisälä Foundation of the Finnish Academy of Science and Letters.

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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

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References

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