北邮数据库课程讲义chapter6.pptVIP

2013.4.11 To check if a relation Ri in a decomposition of R is in BCNF, use the original set of dependencies F that hold on R, but with the following test: for every set of attributes ? ? Ri, check that ?+ (the attribute closure of ?) either includes no attribute of Ri- ?, or includes all attributes of Ri. If the condition is violated by some ??? ? in F, the dependency ??? (?+ - ??) ? Rican be shown to hold on Ri, and Ri violates BCNF. DataBase System Concepts Attribute A is extraneous in ? if A ? ?  and F logically implies (F – {? ? ?}) ? {(? – A) ? ?}. IF F and (F – {? ? ?}) ? {(? – A) ? ?} are equivalent : F? ((F – {? ? ?}) ? {(? – A) ? ?} ) + ， (? – A) ? ?, ? ? (? – A) , ? ? ? (F – {? ? ?}) ? {(? – A) ? ?} ?F+ (? – A) ? ?? F+ (? – A)+ (F) contains ? DataBase System Concepts DataBase System Concepts Attribute A is extraneous in ? if A ? ?  and the set of functional dependencies  (F – {? ? ?}) ? {? ?(? – A)} logically implies F. IF F and (F – {? ? ?}) ? {? ?(? – A)} are equivalent : (F – {? ? ?}) ? {? ?(? – A)} ?F+ ? ? , ? ? (? – A), ? ?(? – A) F? ((F – {? ? ?}) ? {? ?(? – A)} ) + ， ? ? A? ((F – {? ? ?}) ? {? ?(? – A)} ) + ?+ ((F – {? ? ?}) ? {? ?(? – A)} ) contains A DataBase System Concepts Given F = {A ? C, AB ? C } B is extraneous in AB ? C because A ? C logically implies AB ? C. A+(F)={A,C} contains C Given F = {A ? C, AB ? CD} C is extraneous in AB ? CD since A ? C can be inferred even after deleting C AB+{A ? C, AB ? D}={A,B,C,D} Contains C DataBase System Concepts Testing Extraneous Attributes Consider a set F of functional dependencies and the functional dependency ? ? ? in F. To test if attribute A ? ? is extraneous in ? compute (? –A)+ using the dependencies in F check that (? –A)+ (F) contains ?; if it does, A is extraneous To test if attribute A ? ? is extraneous in ? compute ?+ using only the dependencies in  F’ = (F – {? ? ?}) ? {? ?(? – A)}, check that ?+ (F’) contains A; if it do