State-of-the-art model counters are based on exhaustive DPLL algorithms, and have been successfully used in probabilistic reasoning, one of the key problems in AI. In this article, we present a new exhaustive DPLL algorithm with a formal semantics, a proof of correctness, and a modular design. The modular design is based on the separation of the core model counting algorithm from SAT solving techniques. We also show that the trace of our algorithm belongs to the language of Sentential Decision Diagrams (SDDs), which is a subset of Decision-DNNFs, the trace of existing state-of-the-art model counters. Still, our experimental analysis shows comparable results against state-of-the-art model counters. Furthermore, we obtain the first top-down SDD compiler, and show orders-of-magnitude improvements in SDD construction time against the existing bottom-up SDD compiler.

The sentential decision diagram (SDD) has been recently proposed as a new  tractable representation of Boolean functions that generalizes the influential  ordered binary decision diagram (OBDD).  Empirically, compiling CNFs into SDDs  has yielded significant improvements in both time and space over compiling  them into OBDDs, using a bottom-up compilation approach. In this work, we present a top-down CNF to SDD compiler that is based on techniques  from the SAT literature. We compare the presented compiler empirically to the state-of-the-art, bottom-up SDD compiler, showing orders-of-magnitude improvements in compilation time.