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Distributed Model Checking on Graphs of Bounded Treedepth

Authors Fedor V. Fomin , Pierre Fraigniaud , Pedro Montealegre , Ivan Rapaport , Ioan Todinca

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ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Theory of computation → Verification by model checking
Keywords
  • proof-labeling schemes
  • local computing
  • CONGEST model

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Abstract

We establish that every monadic second-order logic (MSO) formula on graphs with bounded treedepth is decidable in a constant number of rounds within the CONGEST model. To our knowledge, this marks the first meta-theorem regarding distributed model-checking. Various optimization problems on graphs are expressible in MSO. Examples include determining whether a graph G has a clique of size k, whether it admits a coloring with k colors, whether it contains a graph H as a subgraph or minor, or whether terminal vertices in G could be connected via vertex-disjoint paths. Our meta-theorem significantly enhances the work of Bousquet et al. [PODC 2022], which was focused on distributed certification of MSO on graphs with bounded treedepth. Moreover, our results can be extended to solving optimization and counting problems expressible in MSO, in graphs of bounded treedepth.

Cite As Get BibTex

Fedor V. Fomin, Pierre Fraigniaud, Pedro Montealegre, Ivan Rapaport, and Ioan Todinca. Distributed Model Checking on Graphs of Bounded Treedepth. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.DISC.2024.25

Author Details

Fedor V. Fomin
  • University of Bergen, Norway
Pierre Fraigniaud
  • IRIF, Université Paris Cité and CNRS, Paris, France
Pedro Montealegre
  • Universidad Adolfo Ibañez, Santiago, Chile
Ivan Rapaport
  • Universidad de Chile, Santiago, Chile
Ioan Todinca
  • LIFO, Université d'Orléans, France
  • INSA Centre-Val de Loire, Orléans, France

Funding

  • Fomin, Fedor V.: the research leading to these results has received funding from the Research Council of Norway via the project BWCA (grant no. 314528).
  • Fraigniaud, Pierre: partially supported by the ANR projects DUCAT (ANR-20-CE48-0006), and QuData (ANR-18-CE47-0010).
  • Montealegre, Pedro: P.M. has received funding from FONDECYT 1230599.
  • Rapaport, Ivan: I.R. has received funding from FB210005, BASAL funds for centers of excellence from ANID- Chile, and FONDECYT 1220142.

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