The inhibition spectrum and the achievement of causal consistency

Summary.

 We consider the problem of distinguishing causally-consistent global states in asynchronous distributed systems. Such states are fundamental to asynchronous systems, because they correspond to possible simultaneous global states; their detection arises in a variety of distributed applications, including global checkpointing, deadlock detection, termination detection, and broadcasting. A consistent-cut protocol is a protocol which in every run will designate for each processor a state, in such a way that these states together form a consistent cut. We analyze the cost of achieving causal consistency in terms of the extent to which a consistent-cut protocol delays events of the underlying system. We refer to the delaying action of a protocol as inhibition. A protocol using local inhibition may cause the delay of some of a processor’s events until that processor has performed some number of local actions; a protocol using global inhibition may force the delay of some of a processor’s events until that processor has received some communication from other processors. Based on a variety of system and protocol characteristics, including the ability to locally or globally inhibit particular types of events, we give three impossibility results and examine some existing protocols. We are then able to present a thirty-six case summary of protocols and impossibility results for the determination of causally-consistent states as a function of those characteristics. In particular, we demonstrate that local inhibition is necessary and sufficient to solve this problem for general FIFO systems, while global send inhibition is necessary and sufficient for general non-FIFO systems.