Vardi, Moshe Y2019-05-172019-05-172017-122017-11-07December 2Shrotri, Aditya Aniruddha. "On Hashing-Based Approaches to Approximate DNF-Counting." (2017) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/105582">https://hdl.handle.net/1911/105582</a>.https://hdl.handle.net/1911/105582Propositional 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.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Model CountingDNF FormulasHash FunctionsThesis2019-05-17