Abstract
The design of data parallel algorithms for fine-grain machines is a fundamental domain in today′s computer science. High standards in the specification and resolution of problems have been achieved in the sequential case. It seems reasonable to apply the same level of quality to data parallel programs. It appears that most data parallel problems can be specified in terms of pre- and postconditions. These conditions characterize the overall state of the fine-grain processors in the initial and final states. In this paper: • We present an axiomatic system to prove correctness of data parallel algorithms on single-instruction multiple-data (SIMD) machines. • We specify some data parallel problems like tree sum, root finding, radix sorting, and dynamic memory allocation. • With this set of axioms we prove the correctness of programs solving the problems above. It seems that the framework for data parallel problems is quite different from those for problems of parallelism with multiple threads of control, like those solvable in Communicating Sequential Processes (CSP).
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