define the canonical coverans a canonical cover

Question

Define the Canonical cover

Ans: A canonical cover F_c for F is a set of dependencies like F logically implies all dependencies in F_c, and F_c logically entails all dependencies in F. F_c must have the subsequent properties:

• No functional dependency in F_c consists of extraneous attribute
• Every left side of a functional dependency in F_c is unique. Which is, there are no two dependencies α₁→ β₁ and α₂→β₂ in F_c such that α₁ = α₂.

 F_c is minimal in certain sense - it does not consist of extraneous attributes, and it combines functional dependencies with similar left side. It is cheaper to test F_c than it is to test F itself.