On the Probabilistic Omission Adversary

This paper newly proposes a novel round-based synchronous system suffering crash and probabilistic omission failures. In this model, a novel class of adversaries, called p-probabilistic omission adversary (pPOA) is introduced. In addition to the ability of complete control of the crash-failure behavior, p-POA can select any subset of all transmitted messages as omission candidates. Then, each message in the omission candidates is lost with probability p. This paper investigates the feasiblity and complexity of the consensus problem under p-POA. We first show two impossibility results that (1) for any p > 0, there exists no uniform consensus algorithm tolerating more than or equal to n/2 crash failures, and that (2) for any p > 0, any uniform consensus algorithm cannot halt. We also show two consensus algorithms CPO and F-CPO. Both algorithms work under (1/2)-POA and respectively have distinct advantages. The algorithm CPO can tolerate at most n/2− 1 crash failures and achieves O(f) expected round complexity, where f is the actual number of crash failures. This implies that CPO has maximum crashfailure resiliency. While the second algorithm F-CPO assumes the maximum number of crash failures less than n/3, it achieves f +O(1) round compexity in expectation. Since it is known that the lower bound for crash-tolerant consensus is f +1, this result implies that only a constant number of extra rounds is nessesary to tolerate a drastic number of message omissions.