Two definitions for functional dependency.
Date: 29 Mar 2007 13:56:27 -0700
Given a relation R(x,y) when does x->y functional dependency holds? Let's try several relational algebra expressions over R.
- Self join: R /\ R. It evaluates trivially to R. We have to rename at least one variable to get an interesting expression. Here are 2 choces, rename x, or rename y. Let's consider renaming y first:
2a. R(x,y') /\ R(x,y"). Let's join it with the relation y'!=y". The x-
2b. R(x',y) /\ R(x",y). Let's project this relation to <x',x">. The
x->y holds iff the resulting relation is an equivalence relation.
>y holds iff the resulting relation is empty. This cute formulation
has been already discussed on this forum. What is new (at least for me), is the option 2b:
2b. R(x',y) /\ R(x",y). Let's project this relation to <x',x">. The x->y holds iff the resulting relation is an equivalence relation.Received on Thu Mar 29 2007 - 22:56:27 CEST