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When is a functional dependency F said to be minimal?
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Ø Every dependency in F has a single attribute for its right hand side.

Ø We cannot replace any dependency X A in F with a dependency Y A where Y is a proper subset of X and still have a set of dependency that is equivalent to F.

Ø We cannot remove any dependency from F and still have set of dependency that is equivalent to F.
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It is based on concept of full functional dependency. A functional dependency X Y is full functional dependency if removal of any attribute A from X means that the dependency does not hold any more.

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QTP has some additional functionality which is not present in WinRunner. For example,you can test(Functionality and Regression testing) an application developed in .Net technology with QTP,which is not possible to test in WinRunner
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It is a process of analysing the given relation schemas based on their Functional Dependencies (FDs) and primary key to achieve the properties

Ø Minimizing redundancy

Ø Minimizing insertion, deletion and update anomalies.
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A Functional dependency is denoted by X Y between two sets of attributes X and Y that are subsets of R specifies a constraint on the possible tuple that can form a relation state r of R. The constraint is for any two tuples t1 and t2 in r if t1[X] = t2[X] then they have t1[Y] = t2[Y]. This means the value of X component of a tuple uniquely determines the value of component Y.
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Multivalued dependency denoted by X Y specified on relation schema R, where X and Y are both subsets of R, specifies the following constraint on any relation r of R: if two tuples t1 and t2 exist in r such that t1[X] = t2[X] then t3 and t4 should also exist in r with the following properties

Ø t3[x] = t4[X] = t1[X] = t2[X]

Ø t3[Y] = t1[Y] and t4[Y] = t2[Y]

Ø t3[Z] = t2[Z] and t4[Z] = t1[Z]

where [Z = (R-(X U Y)) ]
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