Multiprocessor Simulation Strategies with Optimal Speed-up

Abstract In this paper we consider 2-processor algorithms for simulating the behaviour of given formulae over the basis ⊕, where ⊕ denotes the two argument Boolean function, Exclusive-Or. A sequence of 2-processor simulation strategies 〈Sr〉 (r ⩾ 0) is described and it is proved that the ratio ex r [n] n approach 0.5, where exr[n] is the expected number of steps taken by Sr on n-node formulae generated at random using the binary search tree distribution.