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The following problem is called the everywhere-cover problem:“Given a set of dependencies over adatabase scheme,is the set of dependencies explicitly given for each relation scheme equivalent to thedependencies implied for that relation scheme?”It is shown that when the everywhere-cover problem hasa ‘yes’ answer,examining only the dependencies explicitly given will suffice to test 3NF,BCNF and4NF of a database scheme.But this does not hold for 2NF.Consequently,in such cases,tests ofBCNF and 4NF all take polynomial time.Then a proof is given that test of 3NF of a database schemeis Co-NP-complete,and from this result it is shown that everywhere-cover is also Co-NP-complete whenonly functional dependencies are allowed.These results lead to doubt the truth of the well believed conjec-ture that no polynomial time algorithm for designing a Iossless BCNF database scheme is likely to exist.
The following problem is called the everywhere-cover problem: “Given a set of dependencies over adatabase scheme, is the set of dependencies explicitly given for each relation scheme equivalent to the dedendencies implied for that relation scheme?” It is shown that when the everywhere- cover problem hasa ’yes’ answer, examining only the dependencies who given given suffix to test 3NF, BCNF and4NF of a database scheme.But this does not hold for 2NF.Consequently, in such cases, tests ofBCNF and 4NF all take polynomial time. Then a proof is given that test of 3NF of a database schemeis Co-NP-complete, and from this result it is shown that everywhere-cover is also Co-NP-complete whenonly functional dependencies are allowed .sese results lead to doubt the truth of the well believed conjec-ture that no polynomial time algorithm for designing a Iossless BCNF database scheme is likely to exist.