{"type":"ScholarlyArticle","title":"Counting, Sampling, and Synthesis: The Quest for Scalability","authors":[{"name":"Kuldeep S. Meel","slug":"kuldeep-s-meel","given":"Kuldeep S.","family":"Meel","affiliation":"National University of Singapore"}],"abstract":"The current generation of symbolic reasoning techniques excel at the qualitative tasks (i.e., when the answer is Yes or No); such techniques sufficed for traditional systems whose design sought to achieve deterministic behavior. In contrast, modern computing systems crucially rely on the statistical methods to account for the uncertainty in the environment, and to reason about behavior of these systems, there is need to look beyond qualitative symbolic reasoning techniques. We will discuss our work focused on the development of the  next generation of automated reasoning techniques that can perform higher-order tasks such as quantitative measurement, sampling of representative behavior, and automated synthesis of  systems.  \r\n\r\n\r\nFrom a core technical perspective, our work builds on the SAT revolution, which refers to algorithmic advances in combinatorial solving techniques for the fundamental problem of \r\nsatisfiability (SAT), i.e., whether it is possible to satisfy a given set of constraints. The SAT revolution offers the opportunity to develop scalable techniques for problems that lie beyond SAT from complexity perspective and, therefore, stand to benefit from the availability of powerful SAT engines. \r\nOur work seeks to enable a  Beyond SAT revolution via design of scalable techniques for three fundamental problems that lie beyond SAT:\r\n constrained counting, constrained sampling, and   automated synthesis.","doi":"10.24963/ijcai.2022/817","url":"https://ijcai.org/proceedings/2022/817","pdf":"https://ijcai.org/proceedings/2022/0817.pdf","markdown":"https://ijcai.org/proceedings/2022/817.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/817","volume":{"slug":"2022","title":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2022","url":"https://ijcai.org/proceedings/2022/","year":2022,"location":"Vienna","dates":"23-29 July 2022","editors":"Luc De Raedt","isbn":"978-1-956792-00-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2022"},"section":"Early Career","track":"Early Career","number":817,"pages":{"first":5816,"last":5820},"keywords":["EC: Constraint Satisfaction And Optimization","EC: Knowledge Representation And Reasoning"],"videos":[],"references":[{"position":1,"raw":"[Agrawal et al., 2020] D. 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In Proc. of VMCAI, 2018.","title":"Scalable approximation of quantitative information flow in programs","authors":"F Biondi, M Enescu, A Heuser, A Legay, K S Meel, J Quilbeuf","year":"2018","venue":"Proc. of VMCAI","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Carter and Wegman, 1977] L. J. Carter and M. N Wegman. Universal classes of hash functions. In Proc. of STOC, 1977.","title":"Universal classes of hash functions","authors":"L J Carter, M N Wegman","year":"1977","venue":"Proc. of STOC","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Chakraborty and Meel, 2019] S. Chakraborty and K. S. Meel. On testing of uniform samplers. In Proc. of AAAI, 2019.","title":"On testing of uniform samplers","authors":"S Chakraborty, K S Meel","year":"2019","venue":"Proc. of AAAI","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Chakraborty et al., 2013a] S. Chakraborty, K. S. Meel, and M. Y. Vardi. A scalable and nearly uniform generator of sat witnesses. In Proc. of CAV, 2013.","title":"A scalable and nearly uniform generator of sat witnesses","authors":"Chakraborty","year":"2013","venue":"Proc. of CAV","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Chakraborty et al., 2013b] S. Chakraborty, K. S. Meel, and M. Y. Vardi. A scalable approximate model counter. In Proc. of CP, 2013.","title":"A scalable approximate model counter","authors":"Chakraborty","year":"2013","venue":"Proc. of CP","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Chakraborty et al., 2014a] S. Chakraborty, D. J. Fremont, K. S. Meel, S. A. Seshia, and M. Y. Vardi. Distribution- aware sampling and weighted model counting for SAT. In Proc. of AAAI, 2014.","title":"Distributionaware sampling and weighted model counting for SAT","authors":"Chakraborty","year":"2014","venue":"Proc. of AAAI","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Chakraborty et al., 2014b] S. Chakraborty, K. S. Meel, and M. Y. Vardi. Balancing scalability and uniformity in sat- witness generator. In Proc. of DAC, 2014.","title":"Balancing scalability and uniformity in satwitness generator","authors":"Chakraborty","year":"2014","venue":"Proc. of DAC","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Chakraborty et al., 2015] S. Chakraborty, D. J Fremont, K. S. Meel, and Moshe Y Seshia, S. A.and Vardi. On par- allel scalable uniform sat witness generation. In Proc. of TACAS, 2015.","title":"On parallel scalable uniform sat witness generation","authors":"S Chakraborty, D Fremont, K S Meel, Moshe Y Seshia, S A Vardi","year":"2015","venue":"Proc. of TACAS","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Chakraborty et al., 2016a] S. Chakraborty, K. S. Meel, R. Mistry, and M. Y. Vardi. Approximate probabilistic in- ference via word-level counting. In Proc. of AAAI, 2016.","title":"Approximate probabilistic inference via word-level counting","authors":"Chakraborty","year":"2016","venue":"Proc. of AAAI","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Chakraborty et al., 2016b] S. Chakraborty, K. S. Meel, and M. Y. Vardi. Algorithmic improvements in approximate counting for probabilistic inference: From linear to loga- rithmic sat calls. In Proc. of IJCAI, 2016.","title":"Algorithmic improvements in approximate counting for probabilistic inference: From linear to logarithmic sat calls","authors":"Chakraborty","year":"2016","venue":"Proc. of IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2016/503"},{"position":15,"raw":"[Dudek et al., 2020] Jeffrey M. Dudek, Dror Fried, and K. S. Meel. Taming discrete integration via the boon of dimen- sionality. In Proc. of NeurIPS, 12 2020.","title":"Taming discrete integration via the boon of dimensionality","authors":"Jeffrey M Dudek, Dror Fried, K S Meel","year":"2020","venue":"Proc. of NeurIPS","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Duenas-Osorio et al., 2017] L. Duenas-Osorio, K. S. Meel, R. Paredes, and M. Y. Vardi. Counting-based reliability estimation for power-transmission grids. In Proc. of AAAI, 2017.","title":"Counting-based reliability estimation for power-transmission grids","authors":"L Duenas-Osorio, K S Meel, R Paredes, M Y Vardi","year":"2017","venue":"Proc. of AAAI","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Ghosh and Meel, 2019] B. Ghosh and K. S. Meel. Imli: An incremental framework for maxsat-based learning of inter- pretable classification rules. In Proc. of AIES, 2019.","title":"Imli: An incremental framework for maxsat-based learning of interpretable classification rules","authors":"B Ghosh, K S Meel","year":"2019","venue":"Proc. of AIES","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Golia et al., 2020] P. Golia, S. Roy, and K. S. Meel. Man- than: A data-driven approach for boolean function synthe- sis. In Proc. of CAV, 2020.","title":"Manthan: A data-driven approach for boolean function synthesis","authors":"P Golia, S Roy, K S Meel","year":"2020","venue":"Proc. of CAV","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Golia et al., 2021a] P. Golia, S. Roy, and K. S. Meel. Pro- gram synthesis as dependency quantified formula modulo theory. In Proc. of IJCAI, 2021.","title":"Program synthesis as dependency quantified formula modulo theory","authors":"Golia","year":"2021","venue":"Proc. of IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2021/261"},{"position":20,"raw":"[Golia et al., 2021b] P. Golia, Friedrich Slivovsky, S. Roy, and K. S. Meel. Engineering an efficient boolean func- tional synthesis engine. In Proc. of ICCAD, 2021.","title":"Engineering an efficient boolean functional synthesis engine","authors":"Golia","year":"2021","venue":"Proc. of ICCAD","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Golia et al., 2021c] P. Golia, M. Soos, S. Chakraborty, and K. S. Meel. Designing samplers is easy: The boon of testers. In Proc. of FMCAD, 2021.","title":"Designing samplers is easy: The boon of testers","authors":"Golia","year":"2021","venue":"Proc. of FMCAD","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Jerrum and Sinclair, 1996] M. Jerrum and A. Sinclair. The Markov Chain Monte Carlo method: an approach to ap- proximate counting and integration. Approximation algo- rithms for NP-hard problems, pages 482-520, 1996.","title":"The Markov Chain Monte Carlo method: an approach to approximate counting and integration","authors":"M Jerrum, A Sinclair","year":"1996","venue":"Approximation algorithms for NP-hard problems","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Jerrum et al., 1986] M.R. Jerrum, L.G. Valiant, and V.V. Vazirani. Random generation of combinatorial structures from a uniform distribution. 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In Proc. of Beyond NP Workshop, 2016.","title":"Constrained sampling and counting: Universal hashing meets sat solving","authors":"K S Meel, M Y Vardi, S Chakraborty, D J Fremont, S A Seshia, Dror Fried, Alexander Ivrii, Sharad Malik","year":"2016","venue":"Proc. of Beyond NP Workshop","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Meel et al., 2018] K. S. Meel, Aditya A. Shrotri, and M. Y. Vardi. Not all fprass are equal: Demystifying fprass for dnf-counting. In Proc. of CP, 08 2018.","title":"Not all fprass are equal: Demystifying fprass for dnf-counting","authors":"K S Meel, Aditya A Shrotri, M Y Vardi","year":"2018","venue":"Proc. of CP","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Meel et al., 2020] K. S. Meel, Y. Pote, and S. Chakraborty. On testing of samplers. 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