Question

Difference between canonical cover and minimal cover

Answer 1

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A canonical cover of F is a “minimal” set of functional dependencies equivalent to F, having no redundant dependencies or redundant parts of dependencies .implication in the opposite direction is trivial in each of the cases above, since a (stronger) functional dependency always implies a weaker one a 1)augmentation
2)decomposition
functional dependencies may have redundant dependencies that can be inferred from the others Eg: A → C is redundant in: {A → B, B → C, A → C} Parts of a functional dependency may be redundant EXAMPLE= on RHS {A -B, B -C, A -CD} can be simplified to {A - B, B - C, A - D} EXAMPLE= on LHS: {A - B, B -C, AC - D} can be simplified to {A - B, B -C, A - D} .

MINIMAL COVER

Union Simplification (it is better to do it as soon as possible,

RHS Simplification

LHS Simplification

The set of functional dependencies F covers another set of functional dependencies G,but every set of functional dependencies has a minimal cover. Also, note that there may be more than one minimal cover. Wefind the minimal cover by iteratively simplifying the set of functional dependencies. To do this, we will use three methods. if every functional dependency in G can be inferred from F. More formally, F covers G if G+ ,F+. F is a minimal cover of G if F is the smallest set of functional dependencies that cover G.