Redundancy in Distributed Proofs

Abstract

Distributed proofs are mechanisms enabling 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 data-structures distributed over the nodes (e.g. a spanning tree). We consider well known mechanisms consisting of two components: a prover assigning a certificate to each node, and a distributed algorithm called 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 for establishing perfect tradeoffs between the size of the certificate stored at every node, and the number of rounds of the verification protocol.