A model counter for constraints over unbounded strings

Abstract

Model counting is the problem of determining the number of solutions that satisfy a given set of constraints. Model counting has numerous applications in the quantitative analyses of program execution time, information flow, combinatorial circuit designs as well as probabilistic reasoning. We present a new approach to model counting for structured data types, specifically strings in this work. The key ingredient is a new technique that leverages generating functions as a basic primitive for combinatorial counting. Our tool SMC which embodies this approach can model count for constraints specified in an expressive string language efficiently and precisely, thereby outperforming previous finite-size analysis tools. SMC is expressive enough to model constraints arising in real-world JavaScript applications and UNIX C utilities. We demonstrate the practical feasibility of performing quantitative analyses arising in security applications, such as determining the comparative strengths of password strength meters and determining the information leakage via side channels.