{"title":"原数的下界","authors":"E. Allender, M. Saks, I. Shparlinski","doi":"10.1109/CCC.1999.766257","DOIUrl":null,"url":null,"abstract":"Recent work by Bernasconi, Damm and Shparlinski proved lower bounds on the circuit complexity of the square-free numbers, and raised as an open question if similar (or stronger) lower bounds could be proved for the set of prime numbers. In this short note, we answer this question affirmatively, by showing that the set of prime numbers (represented in the usual binary notation) is not contained in AC/sup 0/ [p] for any prime p. Similar lower bounds are presented for the set of square-free numbers, and for the problem of computing the greatest common divisor of two numbers.","PeriodicalId":432015,"journal":{"name":"Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)","volume":"40 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1999-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"22","resultStr":"{\"title\":\"A lower bound for primality\",\"authors\":\"E. Allender, M. Saks, I. Shparlinski\",\"doi\":\"10.1109/CCC.1999.766257\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Recent work by Bernasconi, Damm and Shparlinski proved lower bounds on the circuit complexity of the square-free numbers, and raised as an open question if similar (or stronger) lower bounds could be proved for the set of prime numbers. In this short note, we answer this question affirmatively, by showing that the set of prime numbers (represented in the usual binary notation) is not contained in AC/sup 0/ [p] for any prime p. Similar lower bounds are presented for the set of square-free numbers, and for the problem of computing the greatest common divisor of two numbers.\",\"PeriodicalId\":432015,\"journal\":{\"name\":\"Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)\",\"volume\":\"40 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1999-05-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"22\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CCC.1999.766257\",\"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. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CCC.1999.766257","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Recent work by Bernasconi, Damm and Shparlinski proved lower bounds on the circuit complexity of the square-free numbers, and raised as an open question if similar (or stronger) lower bounds could be proved for the set of prime numbers. In this short note, we answer this question affirmatively, by showing that the set of prime numbers (represented in the usual binary notation) is not contained in AC/sup 0/ [p] for any prime p. Similar lower bounds are presented for the set of square-free numbers, and for the problem of computing the greatest common divisor of two numbers.
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
