{"title":"深度4次齐次算术公式的超多项式下界","authors":"N. Kayal, N. Limaye, Chandan Saha, S. Srinivasan","doi":"10.1145/2591796.2591823","DOIUrl":null,"url":null,"abstract":"We show that any depth-4 homogeneous arithmetic formula computing the Iterated Matrix Multiplication polynomial IMMn,d -- the (1, 1)-th entry of the product of d generic n × n matrices -- has size nΩ(log n), if d = Ω (log2 n). More-over, any depth-4 homogeneous formula computing the determinant polynomial Detn -- the determinant of a generic n × n matrix -- has size nΩ(log n).","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"29 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"23","resultStr":"{\"title\":\"Super-polynomial lower bounds for depth-4 homogeneous arithmetic formulas\",\"authors\":\"N. Kayal, N. Limaye, Chandan Saha, S. Srinivasan\",\"doi\":\"10.1145/2591796.2591823\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that any depth-4 homogeneous arithmetic formula computing the Iterated Matrix Multiplication polynomial IMMn,d -- the (1, 1)-th entry of the product of d generic n × n matrices -- has size nΩ(log n), if d = Ω (log2 n). More-over, any depth-4 homogeneous formula computing the determinant polynomial Detn -- the determinant of a generic n × n matrix -- has size nΩ(log n).\",\"PeriodicalId\":123501,\"journal\":{\"name\":\"Proceedings of the forty-sixth annual ACM symposium on Theory of computing\",\"volume\":\"29 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-05-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"23\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the forty-sixth annual ACM symposium on Theory of computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/2591796.2591823\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2591796.2591823","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Super-polynomial lower bounds for depth-4 homogeneous arithmetic formulas
We show that any depth-4 homogeneous arithmetic formula computing the Iterated Matrix Multiplication polynomial IMMn,d -- the (1, 1)-th entry of the product of d generic n × n matrices -- has size nΩ(log n), if d = Ω (log2 n). More-over, any depth-4 homogeneous formula computing the determinant polynomial Detn -- the determinant of a generic n × n matrix -- has size nΩ(log n).
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