Specifying Concurrent Problems: Beyond Linearizability and up to Tasks - (Extended Abstract)

Tasks and objects are two predominant ways of specifying distributed problems. A task specifies for each set of processes (which may run concurrently) the valid outputs of the processes. An object specifies the outputs the object may produce when it is accessed sequentially. Each one requires its own implementation notion, to tell when an execution satisfies the specification. For objects linearizability is commonly used, while for tasks implementation notions are less explored. Sequential specifications are very convenient, especially important is the locality property of linearizability, which states that linearizable objects compose for free into a linearizable object. However, most well-known tasks have no sequential specification. Also, tasks have no clear locality property. The paper introduces the notion of interval-sequential object. The corresponding implementation notion of interval-linearizability generalizes linearizability. Interval-linearizability allows to specify any task. However, there are sequential one-shot objects that cannot be expressed as tasks, under the simplest interpretation of a task. The paper also shows that a natural extension of the notion of a task is expressive enough to specify any interval-sequential object.