{"title":"鸽洞原理的分辨率宽度大小权衡","authors":"Stefan S. Dantchev","doi":"10.1109/CCC.2002.1004337","DOIUrl":null,"url":null,"abstract":"We prove the following two results: (1) There is a resolution proof of the Weak Pigeon-Hole Principle, WPHP/sub n//sup m/of size 2/sup O([n log n/log m]+log m)/ for any number of pigeons m and any number of holes n. (2) Any resolution proof of WPHP/sub n//sup m/ of width (1/16 - /spl epsi/) n/sup 2/ has to be of size 2/sup /spl Omega/(n)/, independently from m.. These results give not only a resolution size-width tradeoff for the Weak Pigeon-Hole Principle, but also almost optimal such trade-off for resolution in general. The upper bound (1) may be of independent interest, as it has been known for the two extreme values of m, m = n + 1 and in = 2/sup /spl radic/(n log n)/, only.","PeriodicalId":193513,"journal":{"name":"Proceedings 17th IEEE Annual Conference on Computational Complexity","volume":"24 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2002-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Resolution width-size trade-offs for the Pigeon-Hole Principle\",\"authors\":\"Stefan S. Dantchev\",\"doi\":\"10.1109/CCC.2002.1004337\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove the following two results: (1) There is a resolution proof of the Weak Pigeon-Hole Principle, WPHP/sub n//sup m/of size 2/sup O([n log n/log m]+log m)/ for any number of pigeons m and any number of holes n. (2) Any resolution proof of WPHP/sub n//sup m/ of width (1/16 - /spl epsi/) n/sup 2/ has to be of size 2/sup /spl Omega/(n)/, independently from m.. These results give not only a resolution size-width tradeoff for the Weak Pigeon-Hole Principle, but also almost optimal such trade-off for resolution in general. The upper bound (1) may be of independent interest, as it has been known for the two extreme values of m, m = n + 1 and in = 2/sup /spl radic/(n log n)/, only.\",\"PeriodicalId\":193513,\"journal\":{\"name\":\"Proceedings 17th IEEE Annual Conference on Computational Complexity\",\"volume\":\"24 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2002-05-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings 17th IEEE Annual Conference on Computational Complexity\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CCC.2002.1004337\",\"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 17th IEEE Annual Conference on Computational Complexity","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CCC.2002.1004337","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Resolution width-size trade-offs for the Pigeon-Hole Principle
We prove the following two results: (1) There is a resolution proof of the Weak Pigeon-Hole Principle, WPHP/sub n//sup m/of size 2/sup O([n log n/log m]+log m)/ for any number of pigeons m and any number of holes n. (2) Any resolution proof of WPHP/sub n//sup m/ of width (1/16 - /spl epsi/) n/sup 2/ has to be of size 2/sup /spl Omega/(n)/, independently from m.. These results give not only a resolution size-width tradeoff for the Weak Pigeon-Hole Principle, but also almost optimal such trade-off for resolution in general. The upper bound (1) may be of independent interest, as it has been known for the two extreme values of m, m = n + 1 and in = 2/sup /spl radic/(n log n)/, only.
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