Projected Model Counting: Beyond Independent Support

Given a system of constraints over set X variables, projected model counting asks us to count satisfying assignments the constraint on subset $$\mathcal {P}$$ X. A key idea used in modern counters is first compute an independent support, say {I}$$ , that often small and then models instead . While this has been effective scaling performance counters, question whether we can benefit by projecting variables beyond not explored. In paper, study show contrary intuition, it be beneficial project even several applications, good upper bound suffices. We such cases, identify called support (UBS), necessarily yet UBS guarantees count. Theoretically, exponentially smaller than smallest support. Our experiments otherwise, UBS-based faster support-based counting, while yielding bounds high quality. Based extensive experiments, find solve many problem instances are reach state-of-the-art counter.