{"title":"限制条件下德摩根公式的收缩","authors":"M. Paterson, Uri Zwick","doi":"10.1109/SFCS.1991.185385","DOIUrl":null,"url":null,"abstract":"It is shown that a random restriction leaving only a fraction in of the input variables unassigned reduces the expected de Morgan formula size of the induced function by a factor of O( in /sup 1.63/). This is an improvement over previous results. The new exponent yields an increased lower bound of approximately n/sup 2.63/ for the de Morgan formula size of a function in P defined by A.E. Andreev (1987). This is the largest lower bound known, even for functions in NP.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"40 3","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"68","resultStr":"{\"title\":\"Shrinkage of de Morgan formulae under restriction\",\"authors\":\"M. Paterson, Uri Zwick\",\"doi\":\"10.1109/SFCS.1991.185385\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It is shown that a random restriction leaving only a fraction in of the input variables unassigned reduces the expected de Morgan formula size of the induced function by a factor of O( in /sup 1.63/). This is an improvement over previous results. The new exponent yields an increased lower bound of approximately n/sup 2.63/ for the de Morgan formula size of a function in P defined by A.E. Andreev (1987). This is the largest lower bound known, even for functions in NP.<<ETX>>\",\"PeriodicalId\":320781,\"journal\":{\"name\":\"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science\",\"volume\":\"40 3\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1991-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"68\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFCS.1991.185385\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.1991.185385","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 68
摘要
结果表明，随机限制只留下一小部分未分配的输入变量，将诱导函数的期望de Morgan公式大小降低了0 (in /sup 1.63/)。这是对以前结果的改进。新的指数为A.E. Andreev(1987)定义的P中的函数的de Morgan公式大小提供了大约n/sup 2.63/的增加下界。这是已知的最大下界，即使对于NP中的函数也是如此
It is shown that a random restriction leaving only a fraction in of the input variables unassigned reduces the expected de Morgan formula size of the induced function by a factor of O( in /sup 1.63/). This is an improvement over previous results. The new exponent yields an increased lower bound of approximately n/sup 2.63/ for the de Morgan formula size of a function in P defined by A.E. Andreev (1987). This is the largest lower bound known, even for functions in NP.<>
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