Redundancy in distributed proofs

• Published in: Distributed computing Vol. 34; no. 2; pp. 113 - 132
• Main Authors: Feuilloley, Laurent, Fraigniaud, Pierre, Hirvonen, Juho, Paz, Ami, Perry, Mor
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2021; Springer Nature B.V; Springer Verlag
• Subjects: Algorithms; Boolean algebra; Computer Communication Networks; Computer Hardware; Computer Science; Computer Systems Organization and Communication Networks; Data Structures and Algorithms; Distributed, Parallel, and Cluster Computing; Graph theory; Nodes; Redundancy; Software Engineering/Programming and Operating Systems; Theory of Computation; Distributed graph algorithms; Proof-labeling schemes; Space-time tradeoffs; Distributed verification; Nondeterminism
• ISSN: 0178-2770; 1432-0452
• DOI: 10.1007/s00446-020-00386-z

Distributed proofs are mechanisms that enable the nodes of a network to collectively and efficiently check the correctness of Boolean predicates on the structure of the network (e.g., having a specific diameter), or on objects distributed over the nodes (e.g., a spanning tree). We consider well known mechanisms consisting of two components: a prover that assigns a certificate to each node, and a distributed algorithm called a verifier that is in charge of verifying the distributed proof formed by the collection of all certificates. We show that many network predicates have distributed proofs offering a high level of redundancy, explicitly or implicitly. We use this remarkable property of distributed proofs to establish perfect tradeoffs between the size of the certificate stored at every node, and the number of rounds of the verification protocol.