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Shrotri  \nA THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE  \nDoctor of Philosophy  \nAPPROVED, THESIS COMMITTEE  \nMoshe Vardi   \nMoshe Vardi (Dec 13, 2021 18:49 CST)  \nMoshe Vardi  \n(Chair) University Professor, Karen Ostrum George Distinguished Service Professor in Computational Engineering, Rice University  \nDevika Subramanian  \nProfessor of Computer Science and Electrical Engineering, Rice University  \nIllya Hicks (Dec 13, 2021 20:08 CST)  \nIllya Hicks  \nProfessor of Computational and Applied Mathematics, Rice University  \nSupratik Chakraborty   \nSupratik Chakraborty (Dec 14, 2021 09:36 GMT+5.5)  \nSupratik Chakraborty  \nBajaj Chair Professor in Department of Computer Science and Engineering, IIT Bombay  \nHOUSTON, TEXAS May 2022  \nABSTRACT  \nDomain-Driven Approaches for Constrained Counting and Sampling  \nby  \nAditya A. Shrotri  \nConstrained Counting and Sampling are two fundamental problems in Computer Science, where the task is to count the number of solutions or satisfying assignments toa 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 e􀀋ort has been disjointed, resulting in signi􀀌cant 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. Speci􀀌cally, we develop 􀀍exible techniques that natively exploit the structure inherent in domain-speci􀀌c constraints. This often leads to signi􀀌cant performance gains over the popular approach which attempts to shoehorn all constraints to 􀀌t 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  \nanalyses reveal a nuanced picture wherein our approaches are seen to be a valuable addition to an algorithmic portfolio.  \nAcknowledgments  \nI am deeply grateful to my adviser, Moshe Vardi, for patiently guiding me on `my terms'. He gave me immense freedom to pursue research directions of my interest, while making sure I didn't veer too much o􀀋 course. His constant support and availability for his students, despite a huge number of commitments, is extraordinary. From him, I continue to learn how to see the big picture while being rigorous on the details as well as `thinking fast and slow'. I am excited to continue exploring ideas and directions with him.  \nI also want to thank my other committee members, { Supratik Chakraborty, Illya Hicks and Devika Subramanian { for insightful feedback during my proposal and defense. Their suggestions shaped a collection of projects into a dissertation.  \nI want to thank Supratik Chakraborty both as a close collaborator and mentor as well as for hosting me as a visiting student for a semester at IIT Bombay. I am very lucky to have found support from someone with such technical expertise as well as the time (at the oddest hours) and patience to guide me through the trenches of research.  \nI am also grateful to Kuldeep Meel and Nina Narodytska as collaborators, friends and mentors during di􀀋erent stages of my Ph.D. I could not have asked for a better o􀀎cemate than Kuldeep, during the 􀀌rst couple of years. I enjoyed and learnt a lot from our discussions, both technical and ","cbCaidZcnsARJyWs","https://ap.wps.com/l/cbCaidZcnsARJyWs","pdf",2837374,232,"English","# Abstract\n## Acknowledgments","[{\"question\":\"What problems does the dissertation focus on?\",\"answer\":\"It focuses on Constrained Counting and Sampling, including counting solutions or satisfying assignments under constraints and sampling solutions uniformly at random.\"},{\"question\":\"Why does the dissertation address a “disconnect” between theory and practice?\",\"answer\":\"Theory algorithms with worst-case polynomial guarantees often do not scale well in practice, while powerful general-purpose AI/formal-method tools can fail to scale on polynomially bounded instances.\"},{\"question\":\"What key idea does the dissertation propose?\",\"answer\":\"It develops flexible techniques that directly exploit the structure of domain-specific constraints, improving performance compared with forcing all constraints into rigid algorithms.\"}]","Domain-Driven Approaches for Constrained Counting and Sampling | PDF",1791089872,585]