Common knowledge and consistent simultaneous coordination

Abstract

There is a very close relationship between common knowledge and simultaneity in synchronous distributed systems. The analysis of several well-known problems in terms of common knowledge has led to round-optimal protocols for these problems, including Reliable Broadcast, Distributed Consensus, and the Distributed Firing Squad problem. These problems require that the correct processors coordinate their actions in some way but place no restrictions on the behaviour of the faulty processors. In systems with benign processor failures, however, it is reasonable to require that the actions of a faulty processor be consistent with those of the correct processors, assuming it performs any action at all. We consider problems requiring consistent, simultaneous coordination. We then analyze these problems in terms of common knowledge in several failure models. The analysis of these stronger problems requires a stronger definition of common knowledge, and we study the relationship between these two definitions. In many cases, the two definitions are actually equivalent, and simple modifications of previous solutions yield round-optimal solutions to these problems. When the definitions differ, however, we show that such problems cannot be solved, even in failure-free executions.