Consensus in the Presence of Overlapping Faults and Total Omission

Understanding the fault tolerance of Byzantine Agreement protocols is an important question in distributed computing. While the setting of Byzantine faults has been thoroughly explored in the literature, the (arguably more realistic) omission fault setting is far less studied. In this paper, we revisit the recent work of Loss and Stern who gave the first protocol in the mixed fault model tolerating t Byzantine faults, s send faults, and r receive faults, when 2t + r + s < n and omission faults do not overlap. We observe that their protocol makes no guarantees when omission faults can overlap, i.e., when parties can simultaneously have send and receive faults. We give the first protocol that overcomes this limitation and tolerates the same number of potentially overlapping faults. We then study, for the first time, the total omission setting where all parties can become omission faulty. This setting is motivated by realworld scenarios where every party may experience connectivity issues from time to time, yet agreement should still hold for the parties who manage to output values. We show the first agreement protocol in this setting with parameters s < n and s+r = n. On the other hand, we prove that there is no consensus protocol for the total omission setting which tolerates even a single overlapping omission fault, i.e., where s+r = n+1 and s > 2, or a broadcast protocol for s + r = n and s > 1 even without overlapping faults.