Multi-writer Consistency Conditions for Shared Memory Objects

Regularity is a shared memory consistency condition that has received considerable attention, notably in connection with quorum-based shared memory. Lamport’s original definition of regularity assumed a single-writer model, however, and is not well-defined when each shared variable may have multiple writers. In this paper, we address this need by formally extending the notion of regularity to a multi-writer model. We give three possible definitions of regularity in the presence of multiple writers. We then present a quorum-based algorithm to implement each of the three definitions and prove them correct. We study the relationships between these definitions and a number of other well-known consistency conditions, and give a partial order describing the relative strengths of these consistency conditions. Finally, we provide a practical context for our results by studying the correctness of two well-known algorithms for mutual exclusion under each of our proposed consistency conditions.