{"title":"组和通用协议的催化分支程序","authors":"Hugo Côté, P. McKenzie","doi":"10.1145/3583085","DOIUrl":null,"url":null,"abstract":"CCCatalytic branching programs (catalytic bps) compute the same n-bit boolean function f at multiple entry points that need to be remembered at the exit nodes of the bp. When a doubly exponential number of entry points is allowed, linear amortized catalytic bp size is known to be achievable for any f. Here a method is introduced that produces a catalytic bp out of a reversible bp and a deterministic dag-like communication protocol. In a multiplicity range as low as linear, approximating a threshold is shown possible at linear amortized cost. In the same low range, computing \\(\\texttt {Maj} \\) and \\(\\texttt {Mod} \\) are shown possible at a cost that beats the brute force repetition of the best known bp for these functions by a polylog factor. In the exponential range, the method yields O(nlog n) amortized cost for any symmetric function.","PeriodicalId":44045,"journal":{"name":"ACM Transactions on Computation Theory","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Catalytic branching programs from groups and general protocols\",\"authors\":\"Hugo Côté, P. McKenzie\",\"doi\":\"10.1145/3583085\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"CCCatalytic branching programs (catalytic bps) compute the same n-bit boolean function f at multiple entry points that need to be remembered at the exit nodes of the bp. When a doubly exponential number of entry points is allowed, linear amortized catalytic bp size is known to be achievable for any f. Here a method is introduced that produces a catalytic bp out of a reversible bp and a deterministic dag-like communication protocol. In a multiplicity range as low as linear, approximating a threshold is shown possible at linear amortized cost. In the same low range, computing \\\\(\\\\texttt {Maj} \\\\) and \\\\(\\\\texttt {Mod} \\\\) are shown possible at a cost that beats the brute force repetition of the best known bp for these functions by a polylog factor. In the exponential range, the method yields O(nlog n) amortized cost for any symmetric function.\",\"PeriodicalId\":44045,\"journal\":{\"name\":\"ACM Transactions on Computation Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-05-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACM Transactions on Computation Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3583085\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Transactions on Computation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3583085","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
Catalytic branching programs from groups and general protocols
CCCatalytic branching programs (catalytic bps) compute the same n-bit boolean function f at multiple entry points that need to be remembered at the exit nodes of the bp. When a doubly exponential number of entry points is allowed, linear amortized catalytic bp size is known to be achievable for any f. Here a method is introduced that produces a catalytic bp out of a reversible bp and a deterministic dag-like communication protocol. In a multiplicity range as low as linear, approximating a threshold is shown possible at linear amortized cost. In the same low range, computing \(\texttt {Maj} \) and \(\texttt {Mod} \) are shown possible at a cost that beats the brute force repetition of the best known bp for these functions by a polylog factor. In the exponential range, the method yields O(nlog n) amortized cost for any symmetric function.