Logic of global synchrony

An intermediate-level specification formalism (i.e., specification language supported by laws and a semantic model), Logs, is presented for PRAM and BSP styles of parallel programming. It extends pre-post sequential semantics to reveal states at points of global synchronization. The result is an integration of the pre-post and reactive-process styles of specification. The language consists of only six commands from which other useful commands can be derived. Parallel composition is simply logical conjunction and hence compositional. A simple predicative semantics and a complete set of algebraic laws are presented. Novel ingredients include the separation, in our reactive context, of the processes for nontermination and for abortion which coincide in standard programming models; the use of partitions, combining the terminating behavior of one program with the nonterminating behavior of another; and a fixpoint operator, the partitioned fixpoint. Our semantics benefits from the recent "healthiness function" approach for predicative semantics. Use of Logs, along with the laws for reasoning about it, is demonstrated on two problems: matrix multiplication (a terminating numerical computation) and the dining philosophers (a reactive computation). The style of reasoning is so close to programming practice that direct transformation from Logs specifications to real PRAM and BSP programs becomes possible.

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