TY - GEN

T1 - Interactive distributed proofs

AU - Kol, Gillat

AU - Oshman, Rotem

AU - Saxena, Raghuvansh R.

N1 - Publisher Copyright:
© 2018 Copyright held by the owner/author(s). Publication rights licensed to ACM.

PY - 2018/7/23

Y1 - 2018/7/23

N2 - Interactive proof systems allow a resource-bounded verifier to decide an intractable language (or compute a hard function) by communicating with a powerful but untrusted prover. Such systems guarantee that the prover can only convince the verifier of true statements. In the context of centralized computation, a celebrated result shows that interactive proofs are extremely powerful, allowing polynomial-time verifiers to decide any language in PSPACE. In this work we initiate the study of interactive distributed proofs: a network of nodes interacts with a single untrusted prover, who sees the entire network graph, to decide whether the graph satisfies some property. We focus on the communication cost of the protocol - the number of bits the nodes must exchange with the prover and each other. Our model can also be viewed as a generalization of the various models of “distributed NP” (proof labeling schemes, etc.) which received significant attention recently: while these models only allow the prover to present each network node with a string of advice, our model allows for back-and-forth interaction. We prove both upper and lower bounds for the new model. We show that for some problems, interaction can exponentially decrease the communication cost compared to a non-interactive prover, but on the other hand, some problems retain non-trivial cost even with interaction.

AB - Interactive proof systems allow a resource-bounded verifier to decide an intractable language (or compute a hard function) by communicating with a powerful but untrusted prover. Such systems guarantee that the prover can only convince the verifier of true statements. In the context of centralized computation, a celebrated result shows that interactive proofs are extremely powerful, allowing polynomial-time verifiers to decide any language in PSPACE. In this work we initiate the study of interactive distributed proofs: a network of nodes interacts with a single untrusted prover, who sees the entire network graph, to decide whether the graph satisfies some property. We focus on the communication cost of the protocol - the number of bits the nodes must exchange with the prover and each other. Our model can also be viewed as a generalization of the various models of “distributed NP” (proof labeling schemes, etc.) which received significant attention recently: while these models only allow the prover to present each network node with a string of advice, our model allows for back-and-forth interaction. We prove both upper and lower bounds for the new model. We show that for some problems, interaction can exponentially decrease the communication cost compared to a non-interactive prover, but on the other hand, some problems retain non-trivial cost even with interaction.

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U2 - 10.1145/3212734.3212772

DO - 10.1145/3212734.3212772

M3 - Conference contribution

AN - SCOPUS:85052450471

SN - 9781450357951

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 255

EP - 264

BT - PODC 2018 - Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing

PB - Association for Computing Machinery

T2 - 37th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2018

Y2 - 23 July 2018 through 27 July 2018

ER -