{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T07:21:37Z","timestamp":1771485697324,"version":"3.50.1"},"publisher-location":"New York, NY, USA","reference-count":35,"publisher":"ACM","license":[{"start":{"date-parts":[[2021,6,15]],"date-time":"2021-06-15T00:00:00Z","timestamp":1623715200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2021,6,15]]},"DOI":"10.1145\/3406325.3451008","type":"proceedings-article","created":{"date-parts":[[2021,6,16]],"date-time":"2021-06-16T01:26:13Z","timestamp":1623806773000},"page":"772-785","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":7,"title":["Kronecker products, low-depth circuits, and matrix rigidity"],"prefix":"10.1145","author":[{"given":"Josh","family":"Alman","sequence":"first","affiliation":[{"name":"Harvard University, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2021,6,15]]},"reference":[{"key":"e_1_3_2_1_1_1","volume-title":"Proceedings of the twenty-sixth annual ACM-SIAM Symposium on Discrete Algorithms (SODA). Pages 218\u2013230","author":"Abboud Amir","year":"2014","unstructured":"Amir Abboud, Ryan Williams, and Huacheng Yu. 2014. More applications of the polynomial method to algorithm design. In Proceedings of the twenty-sixth annual ACM-SIAM Symposium on Discrete Algorithms (SODA). Pages 218\u2013230."},{"key":"e_1_3_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2016.57"},{"key":"e_1_3_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2019.00067"},{"key":"e_1_3_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2015.18"},{"key":"e_1_3_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/3055399.3055484"},{"key":"e_1_3_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611976465.32"},{"key":"e_1_3_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/990308.990311"},{"key":"e_1_3_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.1994.365725"},{"key":"e_1_3_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1137\/0211038"},{"key":"e_1_3_2_1_10_1","doi-asserted-by":"crossref","unstructured":"Ronald De Wolf. 2006. Lower bounds on matrix rigidity via a quantum argument. In International Colloquium on Automata Languages and Programming (ICALP). Pages 62\u201371.","DOI":"10.1007\/11786986_7"},{"key":"e_1_3_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.4086\/toc.2019.v015a008"},{"key":"e_1_3_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/3313276.3316348"},{"key":"e_1_3_2_1_13_1","volume-title":"Fourier and Circulant Matrices Are Not Rigid. In 34th Computational Complexity Conference (CCC).","author":"Dvir Zeev","year":"2019","unstructured":"Zeev Dvir and Allen Liu. 2019. Fourier and Circulant Matrices Are Not Rigid. In 34th Computational Complexity Conference (CCC)."},{"key":"e_1_3_2_1_14_1","volume-title":"Proceedings of the forty-fourth annual ACM Symposium on Theory of Computing (STOC). Pages 479\u2013494","author":"G\u00e1l Anna","unstructured":"Anna G\u00e1l, Kristoffer Arnsfelt Hansen, Michal Kouck\\`y, Pavel Pudl\u00e1k, and Emanuele Viola. 2012. Tight bounds on computing error-correcting codes by bounded-depth circuits with arbitrary gates. In Proceedings of the forty-fourth annual ACM Symposium on Theory of Computing (STOC). Pages 479\u2013494."},{"key":"e_1_3_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcom.1998.0476"},{"key":"e_1_3_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1561\/0400000063"},{"key":"e_1_3_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/2608628.2608664"},{"key":"e_1_3_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(00)00008-6"},{"key":"e_1_3_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.2001.1786"},{"key":"e_1_3_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1561\/0400000011"},{"key":"e_1_3_2_1_21_1","volume-title":"Three lines proof of the lower bound for the matrix rigidity. arXiv preprint cs\/0506081","author":"Midrijanis Gatis","year":"2005","unstructured":"Gatis Midrijanis. 2005. Three lines proof of the lower bound for the matrix rigidity. arXiv preprint cs\/0506081, 2005."},{"key":"e_1_3_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/321752.321761"},{"key":"e_1_3_2_1_23_1","volume-title":"Equivalence of Systematic Linear Data Structures and Matrix Rigidity. In 11th Innovations in Theoretical Computer Science Conference (ITCS).","author":"Ramamoorthy Sivaramakrishnan Natarajan","year":"2020","unstructured":"Sivaramakrishnan Natarajan Ramamoorthy and Cyrus Rashtchian. 2020. Equivalence of Systematic Linear Data Structures and Matrix Rigidity. In 11th Innovations in Theoretical Computer Science Conference (ITCS)."},{"key":"e_1_3_2_1_24_1","volume-title":"Lower bounds on arithmetic circuits via partial derivatives. Computational complexity, 6, 3","author":"Nisan Noam","year":"1996","unstructured":"Noam Nisan and Avi Wigderson. 1996. Lower bounds on arithmetic circuits via partial derivatives. Computational complexity, 6, 3, 1996. Pages 217\u2013234."},{"key":"e_1_3_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01215351"},{"key":"e_1_3_2_1_26_1","volume-title":"A note on the use of determinant for proving lower bounds on the size of linear circuits. Information processing letters, 74, 5-6","author":"Pudl\u00e1k Pavel","year":"2000","unstructured":"Pavel Pudl\u00e1k. 2000. A note on the use of determinant for proving lower bounds on the size of linear circuits. Information processing letters, 74, 5-6, 2000. Pages 197\u2013201."},{"key":"e_1_3_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480197329508"},{"key":"e_1_3_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/509907.509932"},{"key":"e_1_3_2_1_29_1","unstructured":"Igor E. Shparlinski. 1999. 1999."},{"key":"e_1_3_2_1_30_1","volume-title":"Gaussian elimination is not optimal. Numerische mathematik, 13, 4","author":"Strassen Volker","year":"1969","unstructured":"Volker Strassen. 1969. Gaussian elimination is not optimal. Numerische mathematik, 13, 4, 1969. Pages 354\u2013356."},{"key":"e_1_3_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-08353-7_135"},{"key":"e_1_3_2_1_32_1","first-page":"1","article-title":"The ubiquitous Kronecker product","volume":"123","author":"Van Loan Charles F","year":"2000","unstructured":"Charles F Van Loan. 2000. The ubiquitous Kronecker product. Journal of computational and applied mathematics, 123, 1-2, 2000. Pages 85\u2013100.","journal-title":"Journal of computational and applied mathematics"},{"key":"e_1_3_2_1_33_1","volume-title":"Lower Bounds for Matrix Factorization. computational complexity, 30, 1","author":"Volk Ben Lee","year":"2021","unstructured":"Ben Lee Volk and Mrinal Kumar. 2021. Lower Bounds for Matrix Factorization. computational complexity, 30, 1, 2021. Pages 1\u201340."},{"key":"e_1_3_2_1_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/2591796.2591811"},{"key":"e_1_3_2_1_35_1","doi-asserted-by":"publisher","DOI":"10.1145\/2213977.2214056"}],"event":{"name":"STOC '21: 53rd Annual ACM SIGACT Symposium on Theory of Computing","location":"Virtual Italy","acronym":"STOC '21","sponsor":["SIGACT ACM Special Interest Group on Algorithms and Computation Theory"]},"container-title":["Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing"],"original-title":[],"link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3406325.3451008","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3406325.3451008","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T22:01:44Z","timestamp":1750197704000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3406325.3451008"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,15]]},"references-count":35,"alternative-id":["10.1145\/3406325.3451008","10.1145\/3406325"],"URL":"https:\/\/doi.org\/10.1145\/3406325.3451008","relation":{},"subject":[],"published":{"date-parts":[[2021,6,15]]},"assertion":[{"value":"2021-06-15","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}