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.

中文翻译：

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分布式证明中的冗余

分布式证明是一种机制，使网络节点能够共同有效地检查布尔谓词对网络结构（例如，具有特定直径）或分布在节点上的对象（例如，生成树）的正确性. 我们考虑由两个组件组成的众所周知的机制：一个为每个节点分配证书的证明者，以及一个称为验证者的分布式算法，负责验证由所有证书的集合形成的分布式证明。我们表明，许多网络谓词都具有分布式证明，显式或隐式地提供了高水平的冗余。我们使用分布式证明的这一显着特性在每个节点存储的证书大小与验证协议的轮数之间建立完美的权衡。