## Abstract

We address fully-defective asynchronous networks, in which all links are subject to an unlimited number of alteration errors, implying that all messages in the network may be completely corrupted. Despite the possible intuition that such a setting is too harsh for any reliable communication, we show how to simulate any algorithm for a noiseless setting over any fully-defective setting, given that the network is 2-edge connected. We prove that if the network is not 2-edge connected, no non-trivial computation in the fully-defective setting is possible. The key structural property of 2-edge-connected graphs that we leverage is the existence of an oriented (non-simple) cycle that goes through all nodes [Robbins, 1939]. The core of our technical contribution is presenting a construction of such a Robbins cycle in fully-defective networks, and showing how to communicate over it despite total message corruption. These are obtained in a content-oblivious manner, since nodes must ignore the content of received messages.

Original language | English |
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Title of host publication | PODC 2022 - Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing |

Publisher | Association for Computing Machinery |

Pages | 141-150 |

Number of pages | 10 |

ISBN (Electronic) | 9781450392624 |

DOIs | |

State | Published - 20 Jul 2022 |

Event | 41st ACM Symposium on Principles of Distributed Computing, PODC 2022 - Salerno, Italy Duration: 25 Jul 2022 → 29 Jul 2022 |

### Publication series

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

Conference | 41st ACM Symposium on Principles of Distributed Computing, PODC 2022 |
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Country/Territory | Italy |

City | Salerno |

Period | 25/07/22 → 29/07/22 |

### Bibliographical note

Publisher Copyright:© 2022 ACM.

### Funding

Acknowledgements. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 755839. Ran Gelles is supported in part by the Israel Science Foundation (ISF) through Grant No. 1078/17 and the United States-Israel Binational Science Foundation (BSF) through Grant No. 2020277. Gal Sela is supported in part by the Israel Science Foundation (ISF) through Grant No. 1102/21.

Funders | Funder number |
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Horizon 2020 Framework Programme | 755839 |

United States-Israel Binational Science Foundation | 2020277, 1102/21 |

Israel Science Foundation | 1078/17 |

## Keywords

- Robbins' theorem
- fully-defective networks
- noise resilience