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We present a parallel Knuth-Bendiz completion algorithm where the inner loop, deriving the consequences of adding a new rule to the system, is multi-threaded. The selection of the best new rule in the outer loop, and hence the completion strategy, is exactly the same as for the sequential algorithm. Our implementation, which is within the PARSA C-2 parallel symbolic computation system, exhibits good parallel speed-UPS on a standard multi-processor workstation.

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We report on the design, implementation, and performance, of the parallel term-rewriting system PaReDuX. We discuss the parallelization of three term completion procedures: Knuth-Bendix completion, completion modulo AC, and unfailing completion. Our parallelization is strategy-compliant, i.e., the parallel code performs exactly the same work as the sequential code, but the work load is shared by many processors. PaReDuX is designed for shared memory parallel architectures, such as multi-processor workstations, where it shows good performance on a variety of examples.