Atomic Broadcast and Its Use to Achieve Sequential Consistency

Atomic broadcast is a powerful communication primitive, which is applied in a natural way in sequentially consistent implementations of various data structures (see 1]). Unfortunately the atomic broadcast algorithm as presented is incorrect. Here some ways of correcting it are analyzed under assumptions of blocking versus nonblocking communication. Two atomic broadcast algorithms are proposed: one correct if it is used in a blocking manner, the other correct unconditionally. The latter algorithm, when used in the sequentially consistent implementations of data structures proposed in 1], ensures the same time complexity as claimed in the original application. 1. Introduction The overhead of ensuring linearizability versus sequential consistency of shared objects in a message passing system under various realistic timing assumptions is well studied in 1]. This note points out that the algorithms for sequential consistency are awed for the model assumed and corrects the algorithms. The errors are subtle; one hinges on issues involving blocking versus nonblocking communication. Speciically, in the original paper, sequentially consistent implementations of several data structures (read/write registers, queues, stacks) are designed using a communication primitive called atomic broadcast. The operations on the data-structures are assumed to be blocking. However, if atomic broadcast is also assumed to be blocking, then the claimed time complexities of the sequentially consistent implementations do not hold. On the other hand, if atomic broadcast is assumed to be nonblocking, then the broadcast algorithm provided is incorrect. In section 2 the assumptions about the computation model are stated, an atomic broadcast primitive is deened, and the architecture of a memory consistency system that uses atomic