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Two definitions for functional dependency.

From: Aloha Kakuikanu <aloha.kakuikanu_at_yahoo.com>
Date: 29 Mar 2007 13:56:27 -0700
Message-ID: <1175201787.460169.95830@o5g2000hsb.googlegroups.com>


Given a relation R(x,y) when does x->y functional dependency holds? Let's try several relational algebra expressions over R.

  1. 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-
>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 - 15:56:27 CDT

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