Towards Real-Time Approximate Counting

Model counting is the task of counting the number of satisfying assignments of a Boolean formula. Since counting is intractable in general, most applications use (ε, δ)-approximations, where the output is within a (1+ε)-factor of the count with probability at least 1-δ. Many demanding applications make thousands of counting queries, and the state-of-the-art approximate counter, ApproxMC, makes hundreds of calls to SAT solvers to answer a single approximate counting query. The sheer number of SAT calls, poses a significant challenge to the existing approaches. In this work, we propose an approximation scheme, ApproxMC7, that is tailored to such demanding applications with low time limits. Compared to ApproxMC, ApproxMC7 makes 14× fewer SAT calls while providing the same guarantees as ApproxMC in the constant-factor regime. In an evaluation over 2,247 instances, ApproxMC7 solved 271 more and achieved a 2× speedup against ApproxMC.