Probabilistic Analysis Based On Symbolic Game Semantics and Model Counting

Probabilistic program analysis aims to quantify the probability that a given program satisfies a required property. It has many potential applications, from program understanding and debugging to computing program reliability, compiler optimizations and quantitative information flow analysis for security. In these situations, it is usually more relevant to quantify the probability of satisfying/violating a given property than to just assess the possibility of such events to occur. In this work, we introduce an approach for probabilistic analysis of open programs (i.e. programs with undefined identifiers) based on game semantics and model counting. We use a symbolic representation of algorithmic game semantics to collect the symbolic constraints on the input data (context) that lead to the occurrence of the target events (e.g. satisfaction/violation of a given property). The constraints are then analyzed to quantify how likely is an input to satisfy them. We use model counting techniques to count the number of solutions (from a bounded integer domain) that satisfy given constraints. These counts are then used to assign probabilities to program executions and to assess the probability for the target event to occur at the desired level of confidence. Finally, we present the results of applying our approach to several interesting examples and illustrate the benefits they may offer.