{"title":"几乎所有图检验测试复杂度的上界","authors":"O. V. Zubkov, D. Chistikov, A. A. Voronenko","doi":"10.1109/SYNASC.2011.44","DOIUrl":null,"url":null,"abstract":"The concept of a checking test is of prime interest to the study of a variant of exact identification problem, in which the learner is given a hint about the unknown object. A graph F is said to be a checking test for a co graph G iff for any other co graph H there exists an edge in F distinguishing G and H, that is, contained in exactly one of the graphs G and H. It is known that for any co graph G there exists a unique irredundant checking test, the number of edges in which is called the checking test complexity of G. We show that almost all co graphs on n vertices have relatively small checking test complexity of O(n log n). Using this result, we obtain an upper bound on the checking test complexity of almost all read-once Boolean functions over the basis of disjunction and parity functions.","PeriodicalId":184344,"journal":{"name":"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"23 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"An Upper Bound on Checking Test Complexity for Almost All Cographs\",\"authors\":\"O. V. Zubkov, D. Chistikov, A. A. Voronenko\",\"doi\":\"10.1109/SYNASC.2011.44\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The concept of a checking test is of prime interest to the study of a variant of exact identification problem, in which the learner is given a hint about the unknown object. A graph F is said to be a checking test for a co graph G iff for any other co graph H there exists an edge in F distinguishing G and H, that is, contained in exactly one of the graphs G and H. It is known that for any co graph G there exists a unique irredundant checking test, the number of edges in which is called the checking test complexity of G. We show that almost all co graphs on n vertices have relatively small checking test complexity of O(n log n). Using this result, we obtain an upper bound on the checking test complexity of almost all read-once Boolean functions over the basis of disjunction and parity functions.\",\"PeriodicalId\":184344,\"journal\":{\"name\":\"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing\",\"volume\":\"23 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2011-09-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SYNASC.2011.44\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SYNASC.2011.44","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
An Upper Bound on Checking Test Complexity for Almost All Cographs
The concept of a checking test is of prime interest to the study of a variant of exact identification problem, in which the learner is given a hint about the unknown object. A graph F is said to be a checking test for a co graph G iff for any other co graph H there exists an edge in F distinguishing G and H, that is, contained in exactly one of the graphs G and H. It is known that for any co graph G there exists a unique irredundant checking test, the number of edges in which is called the checking test complexity of G. We show that almost all co graphs on n vertices have relatively small checking test complexity of O(n log n). Using this result, we obtain an upper bound on the checking test complexity of almost all read-once Boolean functions over the basis of disjunction and parity functions.