{"title":"用于前缀计算的布尔网络的大小时间复杂度","authors":"G. Bilardi, F. Preparata","doi":"10.1145/28395.28442","DOIUrl":null,"url":null,"abstract":"The prefix problem consists of computing all the products x0x1…xj (j=0, …, N - 1), given a sequence x = (x0, x1, …, xN - 1) of elements in a semigroup. In this paper we completely characterize the size-time complexity of computing prefixes with boolean networks, which are synchronized interconnections of Boolean gates and one-bit storage devices. This complexity crucially depends upon a property of the underlying semigroup, which we call cycle-freedom (no cycle of length greater than one in the Cayley graph of the semigroup). Denoting by S and T size and computation time, respectively, we have S = &THgr;((N/T) log(N/T)), for non-cycle-free semigroups, and S = &THgr;(N/T), for cycle-free semigroups. In both cases, T ∈ [&OHgr;(logN), O(N)].","PeriodicalId":161795,"journal":{"name":"Proceedings of the nineteenth annual ACM symposium on Theory of computing","volume":"25 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1987-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"12","resultStr":"{\"title\":\"Size-time complexity of Boolean networks for prefix computations\",\"authors\":\"G. Bilardi, F. Preparata\",\"doi\":\"10.1145/28395.28442\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The prefix problem consists of computing all the products x0x1…xj (j=0, …, N - 1), given a sequence x = (x0, x1, …, xN - 1) of elements in a semigroup. In this paper we completely characterize the size-time complexity of computing prefixes with boolean networks, which are synchronized interconnections of Boolean gates and one-bit storage devices. This complexity crucially depends upon a property of the underlying semigroup, which we call cycle-freedom (no cycle of length greater than one in the Cayley graph of the semigroup). Denoting by S and T size and computation time, respectively, we have S = &THgr;((N/T) log(N/T)), for non-cycle-free semigroups, and S = &THgr;(N/T), for cycle-free semigroups. In both cases, T ∈ [&OHgr;(logN), O(N)].\",\"PeriodicalId\":161795,\"journal\":{\"name\":\"Proceedings of the nineteenth annual ACM symposium on Theory of computing\",\"volume\":\"25 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1987-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"12\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the nineteenth annual ACM symposium on Theory of computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/28395.28442\",\"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 of the nineteenth annual ACM symposium on Theory of computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/28395.28442","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Size-time complexity of Boolean networks for prefix computations
The prefix problem consists of computing all the products x0x1…xj (j=0, …, N - 1), given a sequence x = (x0, x1, …, xN - 1) of elements in a semigroup. In this paper we completely characterize the size-time complexity of computing prefixes with boolean networks, which are synchronized interconnections of Boolean gates and one-bit storage devices. This complexity crucially depends upon a property of the underlying semigroup, which we call cycle-freedom (no cycle of length greater than one in the Cayley graph of the semigroup). Denoting by S and T size and computation time, respectively, we have S = &THgr;((N/T) log(N/T)), for non-cycle-free semigroups, and S = &THgr;(N/T), for cycle-free semigroups. In both cases, T ∈ [&OHgr;(logN), O(N)].