Symmetric Component Caching for Model Counting on Combinatorial Instances

Given a propositional formula ψ, the model counting problem, also referred to as #SAT, seeks compute number of satisfying assignments (or models) ψ. Modern search-based algorithms are built on conflict-driven clause learning, combined with caching certain subformulas (called components) encountered during search process. Despite significant progress in these over years, state-of-the-art counters often struggle handle large but structured instances that typically arise combinatorial settings. Motivated by observation do not exploit inherent symmetries exhibited such instances, we revisit component architecture employed current and introduce novel scheme focuses identifying symmetric components. We first prove soundness our approach, then integrate it into counter GANAK. Our extensive experiments hard demonstrate resulting counter, SymGANAK, leads improvements GANAK both terms PAR-2 score solved.