{"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}
引用次数: 14
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.
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