Systematic Parameter Decision in Approximate Model Counting

This paper proposes a novel approach to determining the internal parameters of the hashing-based approximate model counting algorithm mathsfApproxMC. In this problem, the chosen parameter values must ensure that mathsfApproxMC is Probably Approximately Correct (PAC), while also making it as efficient as possible. The existing approach to this problem relies on heuristics; in this paper, we solve this problem by formulating it as an optimization problem that arises from generalizing mathsfApproxMC's correctness proof to arbitrary parameter values. Our approach separates the concerns of algorithm soundness and optimality, allowing us to address the former without the need for repetitive case-by-case argumentation, while establishing a clear framework for the latter. Furthermore, after reduction, the resulting optimization problem takes on an exceptionally simple form, enabling the use of a basic search algorithm and providing insight into how parameter values affect algorithm performance. Experimental results demonstrate that our optimized parameters improve the runtime performance of the latest mathsfApproxMC by a factor of 1.6 to 2.4, depending on the error tolerance.