Approximate model counting, sparse XOR constraints and minimum distance
The problem of counting the number of models of a given Boolean formula has numerous applications, including computing the leakage of deterministic programs in Quantitative Information Flow. Model counting is a hard, #P-complete problem. For this reason, many approximate counters have been developed in the last decade, offering formal guarantees of confidence and accuracy. A popular approach is based on the idea of using random XOR constraints to, roughly, successively halving the solution set until no model is left: this is checked by invocations to a SAT solver.