Given a Boolean formula F, the problem of model counting, also referred to as #SAT, seeks to compute the number of solutions of F. Model counting is a fundamental problem with a wide variety of applications ranging from planning, quantified information flow to probabilistic reasoning and the like. The modern #SAT solvers tend to be either based on static decomposition, dynamic decomposition, or a hybrid of the two. Despite dynamic decomposition based #SAT solvers sharing much of their architecture with SAT solvers, the core design and heuristics of dynamic decomposition-based #SAT solvers has remained constant for over a decade. In this paper, we revisit the architecture of the state-of-the-art dynamic decomposition-based #SAT tool, sharpSAT, and demonstrate that by introducing a new notion of probabilistic component caching and the usage of universal hashing for exact model counting along with the development of several new heuristics can lead to significant performance improvement over state-of-the-art model-counters. In particular, we develop GANAK, a new scalable probabilistic exact model counter that outperforms state-of-the-art exact and approximate model counters sharpSAT and ApproxMC3 respectively, both in terms of PAR-2 score and the number of instances solved. Furthermore, in our experiments, the model count returned by GANAK was equal to the exact model count for all the benchmarks. Finally, we observe that recently proposed preprocessing techniques for model counting benefit exact model counters while hurting the performance of approximate model counters.

Uniform sampling has drawn diverse applications in programming languages and software engineering, like in constrained-random verification (CRV), constrained-fuzzing and bug synthesis. The effectiveness of these applications depend on the uniformity of test stimuli generated from a given set of constraints. Despite significant progress over the past few years, the performance of the state of the art techniques still falls short of those of heuristic methods employed in the industry which sacrifice either uniformity or scalability when generating stimuli.In this paper, we propose a new approach to the uniform generation that builds on recent progress in knowledge compilation. The primary contribution of this paper is marrying knowledge compilation with uniform sampling: our algorithm, KUS, employs the state-of-the-art knowledge compilers to first compile constraints into d-DNNF form, and then, generates samples by making two passes over the compiled representation.We show that KUS is able to significantly outperform existing state-of-the-art algorithms, SPUR and UniGen2, by up to 3 orders of magnitude in terms of runtime while achieving a geometric speedup of 1.7× and 8.3× over SPUR and UniGen2 respectively. Also, KUS achieves a lower PAR-21 score, around 0.82× that of SPUR and 0.38× that of UniGen2. Furthermore, KUS achieves speedups of up to 3 orders of magnitude for incremental sampling. The distribution generated by KUS is statistically indistinguishable from that generated by an ideal uniform sampler. Moreover, KUS is almost oblivious to the number of samples requested.

Given a set of constraints F and a user-defined weight function W on the assignment space, the problem of constrained sampling is to sample satisfying assignments of F conditioned on W. Constrained sampling is a fundamental problem with applications in probabilistic reasoning, synthesis, software and hardware testing. Consequently, the problem of sampling has been subject to intense theoretical and practical investigations over the years. Despite such intense investigations, there still remains a gap between theory and practice. In particular, there has been significant progress in the development of sampling techniques when W is a uniform distribution, but such techniques fail to handle general weight functions W. Furthermore, we are, often, interested in Σ 1 1 formulas, i.e., G(X) := ∃Y F (X, Y) for some F ; typically the set of variables Y are introduced as auxiliary variables during encoding of constraints to F. In this context, one wonders whether it is possible to design sampling techniques whose runtime performance is agnostic to the underlying weight distribution and can handle Σ 1 1 formulas? The primary contribution of this work is a novel technique, called WAPS, for sampling over Σ 1 1 whose runtime is agnostic to W. WAPS is based on our recently discovered connection between knowledge compilation and uniform sampling. WAPS proceeds by compiling F into a well studied compiled form, d-DNNF, which allows sampling operations to be conducted in linear time in the size of the compiled form. We demonstrate that WAPS can significantly outperform existing state-of-the-art weighted and projected sampler WeightGen, by up to 3 orders of magnitude in runtime while achieving a geometric speedup of 296× and solving 564 more instances out of 773. The distribution generated by WAPS is statistically indistinguishable from that generated by an ideal weighted and projected sampler. Furthermore, WAPS is almost oblivious to the number of samples requested.

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