Computing Program Reliability Using Forward-Backward Precondition Analysis and Model Counting

The goal of probabilistic static analysis is to quantify the probability that a given program satisfies/violates a required property (assertion). In this work, we use a static analysis by abstract interpretation and model counting to construct probabilistic analysis of deterministic programs with uncertain input data, which can be used for estimating the probabilities of assertions (program reliability). In particular, we automatically infer necessary preconditions in order a given assertion to be satisfied/violated at run-time using a combination of forward and backward static analyses. The focus is on numeric properties of variables and numeric abstract domains, such as polyhedra. The obtained preconditions in the form of linear constraints are then analyzed to quantify how likely is an input to satisfy them. Model counting techniques are employed to count the number of solutions that satisfy given linear constraints. These counts are then used to assess the probability that the target assertion is satisfied/violated. We also present how to extend our approach to analyze non-deterministic programs by inferring sufficient preconditions. We built a prototype implementation and evaluate it on several interesting examples.