# EGD

## Definitions

An *Equality Generating Dependency (EGD)* is a formula of the following form:
\[\phi(x_{1}, \dots, x_{n}) \rightarrow x_{i} = x_{j}\]
where \(1 \leq i,j \leq n\) and \(\phi\) is a conjunctive query.

An *functional dependency (FD)* is a constraint denoted as follows:
\[R : X \rightarrow y\]
where \(R\) is a relation name, X is a subset of the attribute names of \(R\) and \(y\) is an attribute name of \(R\).
This FD means that if two tuples in \(R\) agree on the attributes in \(X\), they must agree on the attribute \(y\).