Unifying Concurrent Objects and Distributed Tasks: Interval-Linearizability.

Tasks and objects are two predominant ways of specifying distributed problems where processes should compute outputs based on their inputs. Roughly speaking, a task specifies, for each set of processes and each possible assignment of input values, their valid outputs. In contrast, an object is defined by a sequential specification. Also, an object can be invoked multiple times by each process, while a task is a one-shot problem. Each one requires its own implementation notion, stating when an execution satisfies the specification. For objects, linearizability is commonly used, while tasks implementation notions are less explored. The article introduces the notion of interval-sequential object, and the corresponding implementation notion of interval-linearizability, to encompass many problems that have no sequential specification as objects. It is shown that interval-sequential specifications are local, namely, one can consider interval-linearizable object implementations in isolation and compose them for free, without sacrificing interval-linearizability of the whole system. The article also introduces the notion of refined tasks and its corresponding satisfiability notion. In contrast to a task, a refined task can be invoked multiple times by each process. Also, objects that cannot be defined using tasks can be defined using refined tasks. In fact, a main result of the article is that interval-sequential objects and refined tasks have the same expressive power and both are complete in the sense that they are able to specify any prefix-closed set of well-formed executions. Interval-linearizability and refined tasks go beyond unifying objects and tasks; they shed new light on both of them. On the one hand, interval-linearizability brings to task the following benefits: an explicit operational semantics, a more precise implementation notion, a notion of state, and a locality property. On the other hand, refined tasks open new possibilities of applying topological techniques to objects.