550_4.7_Testing_for_a_Lossless_Join_default

What is a lossless joint decomposition?

A decomposition into 2 relations that preserves the connections between attributes within tuples.

What is the requirement for a decomposition to be considered lossless?

For every instance 'r' that satisfies the functional dependencies, projecting 'r' over the decomposed relations and joining the resulting instances must reconstruct the original instance 'r'.

How can you prove that a decomposition does not have a lossless join?

By showing an instance that satisfies the functional dependencies for which additional tuples appear in the join of the projections over the decomposed relations.

What simple test can determine if a binary decomposition is lossless?

Check if the intersection of R1 and R2 functionally determines either R1 minus R2 or R2 minus R1.

What are the attributes in the pizza shop schema for R1 and R2?

R1 has 'pizza topping kind' and R2 has 'topping topping kind'.

In the context of the pizza shop decomposition example, what was the intersection of R1 and R2?

The intersection was 'topping kind'.

Did the functional dependencies hold for the pizza shop decomposition of R1 = pizza topping kind and R2 = topping topping kind?

No, neither topping kind functionally determined pizza nor did it functionally determine topping.

What was the second decomposition example in the pizza shop context?

R1 has attributes pizza and topping, and R2 has attributes topping and topping kind.

Does the attribute 'topping' functionally determine 'pizza' in the second decomposition?

No, the closure of 'topping' does not include 'pizza'.

What is the more complicated test for n-ary decompositions called?

The tableau technique.