On Hashing-Based Approaches to Approximate DNF-Counting

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dc.contributor.advisorVardi, Moshe Yen_US
dc.creatorShrotri, Aditya Aniruddhaen_US
dc.date.accessioned2019-05-17T13:20:15Zen_US
dc.date.available2019-05-17T13:20:15Zen_US
dc.date.created2017-12en_US
dc.date.issued2017-11-07en_US
dc.date.submittedDecember 2017en_US
dc.date.updated2019-05-17T13:20:16Zen_US
dc.description.abstractPropositional 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.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationShrotri, 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>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/105582en_US
dc.language.isoengen_US
dc.rightsCopyright 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.en_US
dc.subjectModel Countingen_US
dc.subjectDNF Formulasen_US
dc.subjectHash Functionsen_US
dc.titleOn Hashing-Based Approaches to Approximate DNF-Countingen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentComputer Scienceen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Scienceen_US
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