Lecture 4

Question 1

What is Heath’s Theorem?

Answer 1

If relation R has a set of attributes X (union) Y (union) Z and functional dependency Y –> Z then R == (pi).(X (union) Y) (R) (bowtie) (pi).(Y(union) Z) (R)

Question 2

How to do the Chase test?

Answer 2

1. Write in table, with a.1 etc. to indicate the unknown bits
2. Apply FD’s
3. Continue until one row has all the “true” values

Question 3

What is a problem with the BCNF-decomposition?

Answer 3

It does not preserve all FD’s

Question 4

How to show dependency preservation?

Answer 4

1. Project FD F onto R (already done by BCNF)
2. Take F’ = (union) F.i
3. Notice that by construction F => F’
4. For each FD f in F
   
   4. 1 compute closure of LHS of f under F’
   5. 2 if RHS of f in that closure FD f implied by F’
5. If that holds true for all f in F then F’ => F, and thus DP

Question 5

What does LHS mean?

Answer 5

Left hand side

Question 6

What does RHS mean?

Answer 6

Right hand side

Question 7

What is the algorithm for 3NF?

Answer 7

1. Find minimal basis for FD’s F
2. For each functional dependency x –> A in G, use XA as the schema of the relations in the decomposiion
   3/ If non of the relations schemas from Step 2 is a superkey for R add another relation whose schema is a key for R

Question 8

How to find a 3NF violation in the FD’s?

Answer 8

Any FD where the LHS is not a superkey violates 3NF