Dependency Theory
Does anyone know of a good website, book or any other resources that would explain dependency theory well? I am stuck on a similar question to the one shown bel开发者_JAVA百科ow:
Given
R < A = {P,Q,R,S,T,U,Y },
gamma = {Y->S …(1)
Q->ST….(2)
U-> Y……(3)
S->R …...(4)
RS->T…….(5) }>.
RTP U->T holds
Answer is:
U -> Y -> S -> RS -> T
aug (4) by S S->R
I think you'll need to search for functional dependency instead of dependency theory. Wikipedia has an introductory article on functional dependency. The expression "Y->S" means
- Y determines S, or
- if you know one value for 'Y', you know one value for 'S' (instead of two or three or seven values for 'S'), or
- if two tuples have the same value for 'Y', they'll also have the same value for 'S'
I'm not familiar with all the notation you posted. But I think you're asked to begin with a relation R and a set of functional dependencies gamma numbered 1 to 4 for reference.
Relation R = {P,Q,R,S,T,U,Y }
FD gamma = {Y->S (1)
Q->ST (2)
U-> Y (3)
S->R (4) }
This appears to be the "setup" for several problems. You're then asked to assume this additional functional dependency.
RS->T (5)
Based on the setup and on that additional FD, you're supposed to prove that the functional dependency U->T holds. The lecturer's answer is "U -> Y -> S -> RS -> T", which I think is the chain of inferences the lecturer wants you to follow. You're given U->Y and Y->S to start with, so here's how that specific chain of inference goes.
U->Y and Y->S, therefore U->S. (transitivity, Lecturer's U->Y->S)
S->R, therefore S->RS. (augmentation, an intermediate step)
U->S and S->RS, therefore U->RS. (transitivity, Lecturer's U->Y->S->RS)
U->RS and RS->T, therefore U->T. (transitivity, Lecturer's U->Y->S->RS->T)
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