  Model counting is the problem of computing the number of satisfying
assignments of a given propositional formula. Although exact model counters can
be naturally furnished by most of the knowledge compilation (KC) methods, in
practice, they fail to generate the compiled results for the exact counting of
models for certain formulas due to the explosion in sizes. Decision-DNNF is an
important KC language that captures most of the practical compilers. We propose
a generalized Decision-DNNF (referred to as partial Decision-DNNF) via
introducing a class of new leaf vertices (called unknown vertices), and then
propose an algorithm called PartialKC to generate randomly partial
Decision-DNNF formulas from the given formulas. An unbiased estimate of the
model number can be computed via a randomly partial Decision-DNNF formula. Each
calling of PartialKC consists of multiple callings of MicroKC, while each of
the latter callings is a process of importance sampling equipped with KC
technologies. The experimental results show that PartialKC is more accurate
than both SampleSearch and SearchTreeSampler, PartialKC scales better than
SearchTreeSampler, and the KC technologies can obviously accelerate sampling.
