Barrier synchronisation: Axiomatisation and relaxation

The bulk synchronous parallel (BSP) model is underpinned by a global synchronisation operation. This operation both synchronises processes and updates local stores using asynchronous communications. In this paper a generalised, nondeterministic, substitution axiom (over functions) is identified with BSP barrier synchronisation. Correctness proofs of BSP programs based on the axiom are structurally similar to proofs of correctness of sequential programs. Global synchronisation is often considered to be relatively expensive to implement on distributed architectures for applications having low levels of communications. In an extreme situation a process having no external interactions may have to wait unnecessarily at a barrier. In this paper a form of barrier operation is introduced which is straightforward to reason about and, with a view to increasing the potential for efficient implementation, permits barrier operations to be relaxed through partial uncoupling thereby allowing processes which do not need to synchronise to proceed.