### Abstract

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.

Original language | English (US) |
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Title of host publication | PODC 2018 - Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing |

Publisher | Association for Computing Machinery |

Pages | 255-264 |

Number of pages | 10 |

ISBN (Print) | 9781450357951 |

DOIs | |

State | Published - Jul 23 2018 |

Event | 37th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2018 - Egham, United Kingdom Duration: Jul 23 2018 → Jul 27 2018 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Principles of Distributed Computing |
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### Other

Other | 37th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2018 |
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Country | United Kingdom |

City | Egham |

Period | 7/23/18 → 7/27/18 |

### All Science Journal Classification (ASJC) codes

- Software
- Hardware and Architecture
- Computer Networks and Communications

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## Cite this

*PODC 2018 - Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing*(pp. 255-264). (Proceedings of the Annual ACM Symposium on Principles of Distributed Computing). Association for Computing Machinery. https://doi.org/10.1145/3212734.3212772