Approximate Model Counting

Yong Kiam Tan, Jiong Yang

Abstract: Approximate model counting is the task of approximating the number of solutions to an input formula. This entry formalizes $\mathsf{ApproxMC}$, an algorithm due to Chakraborty et al. with a probably approximately correct (PAC) guarantee, i.e., $\mathsf{ApproxMC}$ returns a multiplicative $(1+\varepsilon)$-factor approximation of the model count with probability at least $1 - \delta$, where $\varepsilon > 0$ and $0 < \delta \leq 1$. The algorithmic specification is further refined to a verified certificate checker that can be used to validate the results of untrusted $\mathsf{ApproxMC}$ implementations (assuming access to trusted randomness).