2021/12/06 by Pierre Fraigniaud, Fraigniaud, Pierre, Pedro Montealegre +5 · 2 citations
Computer Science · Social Sciences · #Access Control and Trust #Cryptography and Data Security #Distributed #FOS: Computer and information sciences #Logic, Reasoning, and Knowledge #Parallel #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.2112.03195
openalex publication_date 2021/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Distributed certification, whether it be proof-labeling schemes, locally checkable proofs, etc., deals with the issue of certifying the legality of a distributed system with respect to a given boolean predicate. A certificate is assigned to each process in the system by a non-trustable oracle, and the processes are in charge of verifying these certificates, so that two properties are satisfied: completeness, i.e., for every legal instance, there is a certificate assignment leading all processes to accept, and soundness, i.e., for every illegal instance, and for every certificate assignment, at least one process rejects. The verification of the certificates must be fast, and the certificates themselves must be small. A large quantity of results have been produced in this framework, each aiming at designing a distributed certification mechanism for specific boolean predicates. This paper presents a "meta-theorem", applying to many boolean predicates at once. Specifically, we prove that, for every boolean predicate on graphs definable in the monadic second-order (MSO) logic of graphs, there exists a distributed certification mechanism using certificates on O(log2n) bits in n-node graphs of bounded treewidth, with a verification protocol involving a single round of communication between neighbors.