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Unformatted text preview: Matt Wagner Database Notes 10/21/2008 Functional Dependencies Functional Dependency constraints on the relationship between attributes in the schema In R, X <= R, Y <= R X Y In all instances of R, if two tuples have the same values in X, then they should have the same values in Y. A Key Relationship is a functional dependency (F.D.) 1) Determined on the schema level, not relational instance e.g. Y depends on X, or X determines Y 2) A generalization of the key concept 3) The initial set of F.D.'s comes from the application / customer / boss / requirements / et al. Ex: SSN (determines) Fname Rules to Derive F.D.'s Subset Property (Axiom of Reflexivity): If Y is a subset of X, then X Y Augmentation (Axiom of Augmentation): If X Y, then XZ YZ Transitivity (Axiom of Transitivity): If X Y and Y Z, then X Z These three constitute a complete set of rules, though more rules may be derived from these three. Ex: R = {A, B, C, G, H, I} F = A B A C CG H CG I B H 1) AH ?? Yes, via transitive. AB>H 2) AGI ?? Yes, via augmentation. AGCG CGI (transitive) 3) CGHI ?? Yes, CGICG replace CG with H, this CGHI "Closure" of F: all possible functional dependencies derived using 3 rules given initial set of F Database Normalization: 2nd Normal Form: (2NF) if and only if, given any candidate key and any attribute that is not a constituent of a candidate key, the nonkey attribute depends upon the whole of the candidate key rather than just a part of it. 3rd Normal Form: (3NF) if and only if both of the following conditions hold: * The relation R (table) is in second normal form (2NF) * Every nonprime attribute of R is nontransitively dependent (i.e. directly dependent) on every key of R. BoyceCodd Normal Form: (BCNF) It is a slightly stronger version of the third normal form (3NF). A table is in BoyceCodd normal form if and only if, for every one of its nontrivial functional dependencies X Y, X is a superkeythat is, X is either a candidate key or a superset thereof. Relationships Among NF's: 1NF (is weaker than) BCNF 2NF 1NF Etc. ...
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This note was uploaded on 07/31/2011 for the course EEL 4852c taught by Professor Tu during the Fall '08 term at University of South Florida  Tampa.
 Fall '08
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