Automatic complexity analysis of logic programs.

Abstract

This dissertation describes research toward automatic complexity analysis of logic programs and its applications. Automatic complexity analysis of programs concerns the inference of the amount of computational resources consumed during program execution, and has been studied primarily in the context of imperative and functional languages. This dissertation extends these techniques to logic programs so that they can handle nondeterminism, namely, the generation of multiple solutions via backtracking. We describe the design and implementation of a (semi)-automatic worst-case complexity analysis system for logic programs. This system can conduct the worst-case analysis for several complexity measures, such as argument size, number of solutions, and execution time. This dissertation also describes an application of such analyses, namely, a runtime mechanism for controlling task granularity in parallel logic programming systems. The performance of parallel systems often starts to degrade when the concurrent tasks in the systems become too fine-grained. Our approach to granularity control is based on time complexity information. With this information, we can compare the execution cost of a procedure with the average process creation overhead of the underlying system to determine at runtime if we should spawn a procedure call as a new concurrent task or just execute it sequentially. Through experimental measurements, we show that this mechanism can substantially improve the performance of parallel systems in many cases. This dissertation also presents several source-level program transformation techniques for optimizing the evaluation of logic programs containing finite-domain constraints. These techniques are based on number-of-solutions complexity information. The techniques include planning the evaluation order of subgoals, reducing the domain of variables, and planning the instantiation order of variable values. This application allows us to solve a problem by starting with a more declarative but less efficient program, and then automatically transforming it into a more efficient program. Through experimental measurements we show that these program transformation techniques can significantly improve the efficiency of the class of programs containing finite-domain constraints in most cases.