Formally Certified Approximate Model Counting

Yong Kiam Tan, Jiong Yang, Mate Soos, Magnus O. Myreen, Kuldeep S. Meel

Abstract: Approximate model counting is the task of approximating the number of solutions to an input Boolean formula. The state-of-the-art approximate model counter for formulas in conjunctive normal form (CNF), \(\textsf{ApproxMC}\), provides a scalable means of obtaining model counts with probably approximately correct (PAC)-style guarantees. Nevertheless, the validity of \(\textsf{ApproxMC}\)’s approximation relies on a careful theoretical analysis of its randomized algorithm and the correctness of its highly optimized implementation, especially the latter’s stateful interactions with an incremental CNF satisfiability solver capable of natively handling parity (XOR) constraints.