Censor-Hillel, Cohen, Gelles, and Sela (PODC 2022 & Distributed Computing 2023) studied fully-defective asynchronous networks, where communication channels may suffer an extreme form of alteration errors, rendering messages completely corrupted. The model is equivalent to content-oblivious computation, where nodes communicate solely via pulses. They showed that if the network is 2-edge-connected, then any algorithm for a noiseless setting can be simulated in the fully-defective setting; otherwise, no non-trivial computation is possible in the fully-defective setting. However, their simulation requires a predesignated leader, which they conjectured to be necessary for any non-trivial content-oblivious task. In this work, we present two results: General 2-edge-connected topologies: First, we show an asynchronous content-oblivious leader election algorithm that quiescently terminates in any 2-edge-connected network with message complexity $O(m \cdot N \cdot \mathsf{ID}_{\min})$, where $m$ is the number of edges, $N$ is a known upper bound on the number of nodes, and $\mathsf{ID}_{\min}$ is the smallest $\mathsf{ID}$. Combined with the above simulation, this result shows that whenever a size bound $N$ is known, any noiseless algorithm can be simulated in the fully-defective model without a preselected leader, fully refuting the conjecture. Unoriented rings: We then show that the knowledge of $N$ can be dropped in unoriented ring topologies by presenting a quiescently terminating election algorithm with message complexity $O(n \cdot \mathsf{ID}_{\max})$ that matches the previous bound. Consequently, this result constitutes a strict improvement over the previous leader election in oriented rings by Frei, Gelles, Ghazy, and Nolin (DISC 2024) and shows that, on rings, fully-defective and noiseless communication are computationally equivalent, with no additional assumptions.

翻译：Censor-Hillel、Cohen、Gelles和Sela（PODC 2022 & Distributed Computing 2023）研究了完全缺陷的异步网络，其中通信信道可能遭受一种极端的篡改错误，导致消息完全损坏。该模型等价于内容无关的计算，其中节点仅通过脉冲进行通信。他们证明，如果网络是2-边连通的，那么任何无噪声设置下的算法都可以在完全缺陷设置中被模拟；否则，在完全缺陷设置中不可能进行任何非平凡的计算。然而，他们的模拟需要一个预先指定的领导者，他们推测这对于任何非平凡的内容无关任务是必要的。在这项工作中，我们提出了两个结果：一般2-边连通拓扑：首先，我们展示了一种异步内容无关的领导者选举算法，该算法在任何2-边连通网络中静默终止，消息复杂度为$O(m \cdot N \cdot \mathsf{ID}_{\min})$，其中$m$是边数，$N$是节点数量的已知上界，$\mathsf{ID}_{\min}$是最小的$\mathsf{ID}$。结合上述模拟，这一结果表明，只要已知规模上界$N$，任何无噪声算法都可以在完全缺陷模型中模拟，而无需预先选定的领导者，从而完全反驳了该猜想。无定向环：然后我们证明，在无定向环拓扑中，可以放弃对$N$的认知，通过提出一种静默终止的选举算法，其消息复杂度为$O(n \cdot \mathsf{ID}_{\max})$，与先前的界限相匹配。因此，这一结果构成了对Frei、Gelles、Ghazy和Nolin（DISC 2024）先前在定向环中领导者选举的严格改进，并表明在环上，完全缺陷通信与无噪声通信在计算上是等价的，无需额外假设。