Wait-free Algorithms: the Burden of the Past

Abstract Herlihy proved that compare-and-set (CAS) is universal in the classical computing system model composed of an a priori known number of processes. For this, he proposed the first universal construction capable of emulating any data structure with a sequential specification. It has recently been proved that CAS is still universal in the infinite arrival computing model, a model where any number of processes can be created on the fly. This paper explores the complexity issues related to the wait-free CAS-based universal constructions. We first prove that CAS does not allow to implement wait-free and linearizable visible objects in the infinite arrival model with a space complexity bounded by the number of active processes. We then show that this lower bound is tight, in the sense that this dependency can be made as low as desired by proposing a wait-free and linearizable universal construction, using the CAS operation, whose space complexity dependancy on the number of ever issued operations is defined by a parameter that can be linked to any unbounded function. This paper also proves that the lower bound obtained for CAS-based algorithms might be avoided by the use of other synchronization primitives. As an example, we explore algorithms based on the memory-to-memory swap special instruction, that exchanges the content of two shared registers. We propose a universal construction based on memory-to-memory swap whose complexity only depends on the contention, and we illustrate how compare-and-set and memory-to-memory swap can be used jointly within a wait-free queue algorithm.