{"title":"计数公理不多项式地模拟计数门","authors":"R. Impagliazzo, Nathan Segerlind","doi":"10.1109/SFCS.2001.959894","DOIUrl":null,"url":null,"abstract":"We give a family of tautologies whose algebraic translations have constant-degree, polynomial size polynomial calculus refutations over Z/sub 2/, but which require superpolynomial size bounded-depth Frege proofs from Count/sub 2/ axioms. This gives a superpolynomial size separation of bounded-depth Frege plus mod 2 counting axioms from bounded-depth Frege plus parity gates. Combined with another result of the authors, it gives the first size (as opposed to degree) separation between the polynomial calculus and Nullstellensatz systems.","PeriodicalId":378126,"journal":{"name":"Proceedings 2001 IEEE International Conference on Cluster Computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2001-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"14","resultStr":"{\"title\":\"Counting axioms do not polynomially simulate counting gates\",\"authors\":\"R. Impagliazzo, Nathan Segerlind\",\"doi\":\"10.1109/SFCS.2001.959894\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We give a family of tautologies whose algebraic translations have constant-degree, polynomial size polynomial calculus refutations over Z/sub 2/, but which require superpolynomial size bounded-depth Frege proofs from Count/sub 2/ axioms. This gives a superpolynomial size separation of bounded-depth Frege plus mod 2 counting axioms from bounded-depth Frege plus parity gates. Combined with another result of the authors, it gives the first size (as opposed to degree) separation between the polynomial calculus and Nullstellensatz systems.\",\"PeriodicalId\":378126,\"journal\":{\"name\":\"Proceedings 2001 IEEE International Conference on Cluster Computing\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-10-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"14\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings 2001 IEEE International Conference on Cluster Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFCS.2001.959894\",\"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 2001 IEEE International Conference on Cluster Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.2001.959894","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Counting axioms do not polynomially simulate counting gates
We give a family of tautologies whose algebraic translations have constant-degree, polynomial size polynomial calculus refutations over Z/sub 2/, but which require superpolynomial size bounded-depth Frege proofs from Count/sub 2/ axioms. This gives a superpolynomial size separation of bounded-depth Frege plus mod 2 counting axioms from bounded-depth Frege plus parity gates. Combined with another result of the authors, it gives the first size (as opposed to degree) separation between the polynomial calculus and Nullstellensatz systems.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
