Browsing by Author "Shrotri, Aditya Aniruddha"

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    Domain-Driven Approaches for Constrained Counting and Sampling
    (2021-12-16) Shrotri, Aditya Aniruddha; Vardi, Moshe Y
    Constrained Counting and Sampling are two fundamental problems in Computer Science, where the task is to count the number of solutions or satisfying assignments to a given set of constraints, or to sample a solution uniformly at random. Counting and sampling along with their approximate and weighted variants have been extensively studied in both theory and practice. However, this research effort has been disjointed, resulting in significant gaps in knowledge. On one hand, algorithms with worst-case polynomial running times are considered to be the gold standard by the theory community, but rarely scale well in practice. On the other hand, powerful general-purpose algorithms and tools developed by the AI and Formal Methods communities often fail to scale on ‘easy’ problems with polynomial upper bounds. The goal of this dissertation is to illuminate and address this disconnect. Specifically, we develop flexible techniques that natively exploit the structure inherent in domain-specific constraints. This often leads to significant performance gains over the popular approach which attempts to shoehorn all constraints to fit a rigid algorithm. Motivated by numerous practical applications and a lack of practically scalable tools with strong theoretical guarantees, we present new solutions for the concrete problems of DNF-Counting, conditional counting, computing the matrix permanent, sampling traces of a transition system and weighted sampling from low-treewidth CNF formulas. Our empirical analyses reveal a nuanced picture wherein our approaches are seen to be a valuable addition to an algorithmic portfolio.
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    On Hashing-Based Approaches to Approximate DNF-Counting
    (2017-11-07) Shrotri, Aditya Aniruddha; Vardi, Moshe Y
    Propositional model counting is a fundamental problem in AI. For DNF formulas, Monte Carlo-based techniques provide a fully polynomial randomized approximation scheme (FPRAS). For CNF constraints, hashing-based techniques are highly successful. It was recently shown that hashing techniques also yield an FPRAS for DNF counting. Our analysis, however, shows that the proposed hashing approach provides poor time complexity compared to the Monte Carlo techniques, for DNF Counting. Given the success of hashing techniques for CNF constraints, it is natural to ask: Can hashing techniques provide an efficient FPRAS for DNF counting? We provide a positive answer to this question. We introduce two novel algorithmic techniques: Symbolic Hashing and Stochastic Cell Counting, and a new family of Row-Echelon hash functions. We design a hashing-based FPRAS of similar complexity (up to polylog factors) as that of prior works. We also provide an empirical comparison of the various approaches.