Efficient computation of fixpoints that arise in abstract interpretation

Abstract

Program analysis is critical to many software engineering tools. However, modern programming languages make use of a number of constructs that greatly complicate dataflow analyses, for example, unrestricted pointers, higher-order functions, and dynamic allocation. Program analyses based on abstract interpretation are a promising means of analyzing these difficult constructs. Unfortunately, abstract interpretation often gives rise to complex and expensive fixpoint computations. If it is to become a practical and widely used technique, the problem of computing these fixpoints efficiently must be addressed and overcome.

This thesis presents techniques for efficiently computing complex program analyses based on abstract interpretation. An entailment model is proposed for guiding fixpoint computations by exploring the dependences induced by an abstract semantic functional. An efficient guided entailment algorithm is presented to order dynamically the evaluations in order to reach the least fixpoint most quickly. A context projection method is then presented to reduce the problem state at each node and eliminate unnecessary evaluations. Experiments have been conducted to show that these two techniques greatly improve the efficiency of fixpoint computations of program analyses in the abstract interpretation framework. Finally, parallel processing is explored as a means to accelerate fixpoint computations. A parallel algorithm based on entailment is presented, and a method is proposed for determining the maximum inherent parallelism of any algorithm based on entailment. We perform experiments in which actual analysis executions are traced, their inherent parallelism is determined, and a post-trace simulation on limited processors is performed. Experiments show that the parallel algorithm we propose realizes the maximum inherent parallelism, given unlimited processors, and performs efficiently on limited processors.