It is well known that an NP oracle does not fully capture the behavior of SAT solvers, as SAT solvers are also designed to provide satisfying assignments when a formula is satisfiable, without additional overhead. Accordingly, the notion of SAT oracle has been proposed to capture the behavior of SAT solver wherein given a Boolean formula, an SAT oracle returns a satisfying assignment if the formula is satisfiable or returns unsatisfiable otherwise.
The primary contribution of this work is to study the relative power of the NP oracle and SAT oracle in the context of approximate model counting. We develop a new methodology to achieve the main result: a SAT oracle is no more powerful than an NP oracle in the context of approximate model counting.
(To appear in ICALP 2023 (https://arxiv.org/abs/2306.10281). Joint work with Diptarka Chakraborty, Sourav Chakraborty, and Kuldeep S. Meel).