J. K. Slaney and E. L. Lusk, "Parallelizing the Closure Computation in Automated Deduction," Preprint ANL/MCS-P123-0190, January 1990. [pdf]
In this paper we present a parallel algorithm for computing the closure of a set under an operation. This particular type of computation appears in a variety of disguises, and has been used in automated theorem proving, abstract algebra, and formal logic. The algorithm we give here is particularly suited for shared-memory parallel computers, where it makes possible economies of space. Implementations of the algorithm in two application contexts are described and experimental results given.