Strengthen, Widen, Get Semaphores

Many parallel programs are expressed in terms of conditional atomic actions with different degrees of atomicity. It is known that these synchronization primitives are expensive to implement in its fully generality [2]. Many platforms provide an efficient set of synchronization primitives. Semaphores are a very special case of conditional atomic actions which can be considered a canonical synchronization primitive. There exist methods to transform general conditional atomic actions into these very special ones. One of the simplest is the Change of Variables method introduced in [1,2] and generalized in [10]. We review and improve this method in the context of formal development of multiprograms [4,7].