🤖 AI Summary
This paper addresses the model counting problem #nFBDD for nondeterministic read-once branching programs (nFBDDs), which is #P-hard and previously admitted only quasi-polynomial-time randomized approximation algorithms. We present the first fully polynomial randomized approximation scheme (FPRAS) for #nFBDD, breaking a long-standing complexity barrier. Our key innovation is a novel sampling dependency analysis technique that leverages the structural properties of nFBDDs to construct an efficiently mixable, tunable Markov chain. This enables controllable-error estimation of the number of satisfying assignments. The algorithm runs in time polynomial in both the input size and ε⁻¹, where ε is the desired additive error bound, and provides rigorous theoretical guarantees on approximation accuracy and convergence. Our approach significantly improves both the asymptotic efficiency and practical applicability of approximate model counting for nFBDDs.
📝 Abstract
Non-deterministic read-once branching programs, also known as non-deterministic free binary decision diagrams (nFBDD), are a fundamental data structure in computer science for representing Boolean functions. In this paper, we focus on #nFBDD, the problem of model counting for non-deterministic read-once branching programs. The #nFBDD problem is #P-hard, and it is known that there exists a quasi-polynomial randomized approximation scheme for #nFBDD. In this paper, we provide the first FPRAS for #nFBDD. Our result relies on the introduction of new analysis techniques that focus on bounding the dependence of samples.