Asynchronous Resilient Linearizability

We address the problem of implementing a distributed data-structure that can tolerate process crash failures in an asynchronous message passing system, while guaranteeing correctness (linearizability with respect to a given sequential specification) and resiliency (the operations are guaranteed to terminate, as long as a majority of the processes do not fail). We consider a class of data-structures whose operations can be classified into two kinds: update operations that can modify the data-structure but do not return a value and read operations that return a value, but do not modify the data-structure. We show that if every pair of update operations commute or nullify each other, then resilient linearizable replication is possible. We propose an algorithm for this class of data-structures with a message complexity of two message round trips for read operations and O(n) round trips for update operations. We also show that if there exists some reachable state where a pair of idempotent update operations neither commute nor nullify each other, resilient linearizable replication is not possible.