## Abstract

In a distributed locally-checkable proof, we are interested in checking the legality of a given network configuration with respect to some Boolean predicate. To do so, the network enlists the help of a prover—a computationally-unbounded oracle that aims at convincing the network that its state is legal, by providing the nodes with certificates that form a distributed proof of legality. The nodes then verify the proof by examining their certificate, their local neighborhood and the certificates of their neighbors. In this paper we examine the power of a randomized form of locally-checkable proof, called distributed Merlin-Arthur protocols, or dMA for short. In a dMA protocol, the prover assigns each node a short certificate, and the nodes then exchange random messages with their neighbors. We show that while there exist problems for which dMA protocols are more efficient than protocols that do not use randomness, for several natural problems, including Leader Election, Diameter, Symmetry, and Counting Distinct Elements, dMA protocols are no more efficient than standard nondeterministic protocols. This is in contrast with Arthur-Merlin (dMA) protocols and Randomized Proof Labeling Schemes (RPLS), which are known to provide improvements in certificate size, at least for some of the aforementioned properties.

Original language | English |
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Title of host publication | Structural Information and Communication Complexity - 26th International Colloquium, SIROCCO 2019, Proceedings |

Editors | Keren Censor-Hillel, Michele Flammini |

Publisher | Springer Verlag |

Pages | 230-245 |

Number of pages | 16 |

ISBN (Print) | 9783030249212 |

DOIs | |

State | Published - 2019 |

Event | 26th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2019 - L'Aquila, Italy Duration: 1 Jul 2019 → 4 Jul 2019 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11639 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 26th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2019 |
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Country/Territory | Italy |

City | L'Aquila |

Period | 1/07/19 → 4/07/19 |

### Funding

Funders | Funder number |
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ISF i-core Center for Excellence | 4/11 |

Tecnol?gicos de Excelencia | AFB 170001 |

ComisiÃ³n Nacional de InvestigaciÃ³n CientÃfica y TecnolÃ³gica | |

Fondo Nacional de Desarrollo CientÃfico y TecnolÃ³gico | 1170021 |

## Keywords

- Distributed verification
- Interactive computation
- Interactive proof systems
- Nondeterminism