{"title":"语法多线性算术电路大小的下界","authors":"R. Raz, Amir Shpilka, A. Yehudayoff","doi":"10.1137/070707932","DOIUrl":null,"url":null,"abstract":"We construct an explicit polynomial f(x<sub>1</sub>,..., x<sub>n</sub>), with coefficients in {0, 1}, such that the size of any syntactically multilinear arithmetic circuit computing f is at least Omega{n<sup>4/3</sup> log<sup>2</sup> n} The lower bound holds over any field.","PeriodicalId":197431,"journal":{"name":"48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2008-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"67","resultStr":"{\"title\":\"A Lower Bound for the Size of Syntactically Multilinear Arithmetic Circuits\",\"authors\":\"R. Raz, Amir Shpilka, A. Yehudayoff\",\"doi\":\"10.1137/070707932\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We construct an explicit polynomial f(x<sub>1</sub>,..., x<sub>n</sub>), with coefficients in {0, 1}, such that the size of any syntactically multilinear arithmetic circuit computing f is at least Omega{n<sup>4/3</sup> log<sup>2</sup> n} The lower bound holds over any field.\",\"PeriodicalId\":197431,\"journal\":{\"name\":\"48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2008-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"67\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/070707932\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/070707932","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Lower Bound for the Size of Syntactically Multilinear Arithmetic Circuits
We construct an explicit polynomial f(x1,..., xn), with coefficients in {0, 1}, such that the size of any syntactically multilinear arithmetic circuit computing f is at least Omega{n4/3 log2 n} The lower bound holds over any field.