Year: 2025
Type: article
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 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. (in: 41st ACM Symposium on Principles of Distributed Computing (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.
Source: Algorithmica
Authors: Fedor V. Fomin, Pierre Fraigniaud, Pedro Montealegre, Ivan Rapaport, Ioan Todinca
Institutions: University of Bergen, Centre National de la Recherche Scientifique, Université Paris Cité, Institut de Recherche en Informatique Fondamentale, Adolfo Ibáñez University, Center for Mathematical Modeling, University of Chile, Université d'Orléans, Institut National des Sciences Appliquées Centre Val de Loire
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
Awards: ENERGY EFFICIENCY IN DISTRIBUTED COMPUTING, UNDERSTANDING GRAPHS AND LOCALITY VIA LOCAL CERTIFICATION, Distributed Network Computing through the Lens of Combinatorial Topology, Energy-Efficient Distributed Computing, G4003710626, COMPACT DISTRIBUTED CERTIFICATION OF HEREDITARY GRAPH CLASSES, Algorithms with predictions, G5399623649, CENTER FOR MATHEMATICAL MODELING (CMM), COMPUTING POWER OF HYBRID MODELS IN SYNCHRONOUS NETWORKS
OpenAlex ID: W4416598571