{"title":"Superlinear lower bounds for bounded-width branching programs","authors":"D. M. Barrington, Howard Straubing","doi":"10.1109/SCT.1991.160274","DOIUrl":null,"url":null,"abstract":"The authors use algebraic techniques to obtain superlinear lower bounds on the size of bounded-width branching programs to solve a number of problems. In particular, they show that any bounded-width branching program computing a nonconstant threshold function has length Omega (n log log n), improving on the previous lower bounds known to apply to all such threshold functions. They also show that any program over a finite solvable monoid computing products in a nonsolvable group has length Omega (n log log n). This result is a step toward proving the conjecture that the circuit complexity class ACC/sup 0/ is properly contained in NC/sup 1/.<<ETX>>","PeriodicalId":158682,"journal":{"name":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","volume":"45 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"45","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SCT.1991.160274","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 45
Abstract
The authors use algebraic techniques to obtain superlinear lower bounds on the size of bounded-width branching programs to solve a number of problems. In particular, they show that any bounded-width branching program computing a nonconstant threshold function has length Omega (n log log n), improving on the previous lower bounds known to apply to all such threshold functions. They also show that any program over a finite solvable monoid computing products in a nonsolvable group has length Omega (n log log n). This result is a step toward proving the conjecture that the circuit complexity class ACC/sup 0/ is properly contained in NC/sup 1/.<>