Why Multi-SLD beats SLD (even on a uniprocessor)

Abstract

Multi-SLD resolution is a variant of SLD resolution based on a simple idea: Let the allowed constraints be closed under disjunction, and provide a mechanism for collecting the solutions to a goal and turning these solutions into a disjunctive constraint. This idea leads to a novel operational model of logic programming, called data or-parallelism, in which multiple constraint environments partially replace backtracking as the operational embodiment of disjunction. The model has a natural implementation on data-parallel computers since each disjunct of a disjunctive constraint can be handled by a single (virtual) processor. In this paper we give linear performance models that explain why Multi-SLD resolution is faster than SLD resolution for many combinatorial search problems, even on a uniprocessor. The models give insight into the nature of data or-parallelism and provide a basis for predicting the effects of various optimizations. We present data from actual uniprocessor and SIMD executions to support the validity of the models. Lastly, we relate the models' predictions to the supposed limits on parallel speedup suggested by Amdahl's Law.