The Instancy of Snapshots and Commuting Objects

We present a sequence of constructions of commuting synchronization objects (e.g., fetch-and-increment and fetch-and-add) in a system of n processors from any two processor synchronization object whose consensus number is two or more Her91a]. Each implementation in the sequence uses a particular type of shared memory snapshot, as a building block. Later implementations in the sequence are based on higher quality snapshots. The rst implementation of a fetch-and-increment uses the standard atomic snapshot concept, introduced in AAD + 93, And90], while the last construction in the sequence, of fetch-and-add, is based on the immediate snapshot concept introduced in BG93b]. This last construction also yields an implementation of a stronger snapshot which we call Write-and-snapshot. In addition this work solves an open question of Borowsky and Gafni by presenting an implementation of a multi-shot immediate snapshot object. Additional implications of our constructions are: (1) The existence of fault-tolerant self implementations of commuting objects, (2) improvements in the eeciency of randomized constructions of commuting objects from read/write registers, and (3) low contention constructions of commuting objects.