Detecting Causality in the Presence of Byzantine Processes: There is No Holy Grail

Abstract

Detecting causality or the happens before relation between events in an asynchronous distributed system is a fundamental building block for distributed applications. To the best of our knowledge, this problem has not been examined in a system with Byzantine processes. We prove the following results for an asynchronous system with Byzantine processes. (1) We prove that it is impossible to determine causality between events in the presence of even a single Byzantine process when processes communicate by unicasting. (2) We also prove a similar impossibility result when processes communicate by broadcasting. (3) We also prove a similar impossibility result when processes communicate by multicasting. (4) In an execution where there exists a causal path between two events passing through only correct processes, the impossibility result for unicasts remains. (5) However, when processes communicate by broadcasting and there exists a causal path between two events passing through only correct processes, it is possible to detect causality between such a pair of events. (6) In an execution where processes communicate by multicasting and there exists a causal path between two events passing through only correct processes, we prove that the impossibility result for multicasts remains.