Synchronization power depends on the register size

Though it is common practice to treat synchronization primitives for multiprocessors as abstract data types, they are in reality machine instructions on registers. A crucial theoretical question with practical implications is the relationship between the size of the register and its computational power. The authors study this question and choose as a first target the popular compare and swap operation (which is the basis for many modern multiprocessor architectures). The results of this paper suggest that a complexity hierarchy for multiprocessor synchronization operations should be based on the space complexity of synchronization registers and not on the number of so called “synchronization objects”