| M.W. Vincent and B. Srinivasan, A Note on Relation Schemes which are in 3NF but not in BCNF, Inf. Process. Lett. 48(1994) 281-283. |
.... for the negative result is that, in this situation, the problem attribute A appears in a key of relation scheme ( U; F ) is already NPcomplete; this result in turn is related to the fact that a relation scheme ( U; F ) can possibly have exponentially many keys [LO78, JF82, MR83, Kat92, VS93a, DKMST95] Theorem 7. For the class of relation schemes ( U; F ) where F is a set of functional dependencies, the problem ( U; F ) is in Boyce Codd normal form is decidable in polynomial time. Indeed, a decision procedure can be based on the following equivalence [Osb78] Boyce Codd ....
M. W. Vincent and B. Srinivasan. A note on relation schemes which are in 3NF but not in BCNF. Information Processing Letters, 48:281--283, 1993.
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M.W. Vincent and B. Srinivasan, A Note on Relation Schemes which are in 3NF but not in BCNF, Inf. Process. Lett. 48(1994) 281-283.
....The reason for 5NF not generalising 4NF originates from the different properties of implied JDs to those of implied MVDs and FDs. MVDs and FDs have the property that if the lhs of every nontrivial dependency in S is a superkey, then the lhs of every nontrivial MVD or FD in S is a superkey [21, 22]. Thus, as noted in Section 1, equivalent definitions of BCNF and 4NF can be obtained if the condition that all dependencies in S have the normal form property is replaced by the requirement that the dependencies in S have the property. However, as the following example and Example 3.1 ....
M.W. Vincent and B. Srinivasan, A Note on Relation Schemes which are in 3NF but not in BCNF, Inf. Process. Lett. 48(1994) 281-283.
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