On the Computational Power of Shared Objects

Abstract

Abstract. We propose a new classification for evaluating the strength of shared objects. The classification is based on finding, for each object of type o, the strongest progress condition for which it is possible to solve consensus for any number of processes, using any number of objects of type o and atomic registers. We use the strongest progress condition to associate with each object a number call the power number of that object. Objects with higher power numbers are considered stronger. Then, we define the power hierarchy which is an infinite hierarchy of objects such that the objects at level i of the hierarchy are exactly those objects with power number i. Comparing our classification with the traditional one which is based on fixing the progress condition (namely, wait-freedom) and finding the largest number of processes for which consensus is solvable, reveals interesting results. Our equivalence and extended universality results, provide a deeper understanding of the nature of the relative computational power of shared objects.

Safety-Liveness Exclusion in Distributed Computing

“…In particular, for shared memory systems, a liveness property states that some process is eventually returned a desirable response, i.e. makes progress [23,25,35]. For each shared object type, there is a property that requires progress for all correct processes, the strongest liveness requirement that can be expected.…”

“…We explore a restricted definition of liveness that covers properties of non-blocking systems and includes properties that require either minimal or maximal progress and which are either dependent or independent of a scheduler. † Our restricted definition combines the notions of k-obstruction-freedom [35] and l-lockfreedom. While k-obstruction-freedom is a dependent maximal progress guarantee that requires progress of every process in a group of less than k processes which execute alone, l-lock freedom is an independent minimal progress guarantee that requires progress of at least l correct processes.…”

The x-Wait-Freedom Progress Condition

“…x-Obstruction-freedom is a generalization of obstruction-freedom [14,15]. It guarantees that, for every set of processes P , |P | ≤ x, every process in P -that does not crash-returns from its operation invocation if no process outside P takes steps for "long enough".…”

“…Let us consider an n-process asynchronous crash-prone system enriched with objects that wait-free solve the consensus problem for a set of x processes, with x < n. It is shown in [15] that, in such a system, it is possible to design an x-obstruction-free implementation of any concurrent object (shared by the n processes) defined by a sequential specification.…”

“…Interestingly, this consensus algorithm is not trivial: it has to solve a competition problem in presence of failures. The universal construction described in [15] (that builds x-obstruction-free concurrent objects) can then be adapted to use the proposed n-process x-wait-free consensus algorithm, in order to build x-wait-free concurrent objects.…”