Precise interprocedural analysis using random interpretation

Abstract

We describe a unified framework for random interpretation that generalizes previous randomized intraprocedural analyses, and also extends naturally to efficient interprocedural analyses. There is no such natural extension known for deterministic algorithms. We present a general technique for extending any intraprocedural random interpreter to perform a context-sensitive interprocedural analysis with only polynomial increase in running time. This technique involves computing random summaries of procedures, which are complete and probabilistically sound.As an instantiation of this general technique, we obtain the first polynomial-time randomized algorithm that discovers all linear relationships interprocedurally in a linear program. We also obtain the first polynomial-time randomized algorithm for precise interprocedural value numbering over a program with unary uninterpreted functions.We present experimental evidence that quantifies the precision and relative speed of the analysis for discovering linear relationships along two dimensions: intraprocedural vs. interprocedural, and deterministic vs. randomized. We also present results that show the variation of the error probability in the randomized analysis with changes in algorithm parameters. These results suggest that the error probability is much lower than the existing conservative theoretical bounds.