Efficient computation of fixpoints that arise in complex program analysis

This paper presents an eecient algorithm for solving the xpoints that arise in complex program analysis based on abstract interpretation. The algorithm behaves like those based upon interval analysis of a ow graph, but without requiring the ow graph to be given a priori. In the general case, the structure of the x-point computation is not known prior to analysis. In the algorithm, the entailment graph, representing the structure of the xpoint computation, is developed during analysis; it is precise and thus results in an eecient analysis. The strategies, which underlie the algorithm, for determining the evaluation order are described. Based on these strategies, local knowledge of the entailment graph at each node is exploited to determine dynamically an eeective order of evaluations. The algorithm is implemented, and experiments are conducted to compare it to other iterative algorithms for solving such problems. The results show that the algorithm is exible, eecient, and consistently better than the others.