Reasoning About FDs (Contd.)

• Computing the closure of a set of FDs can be expensive. (Size of closure is exponential in # attrs!)

• Typically, we just want to check if a given FD X Y is in the closure of a set of FDs F. An efficient check:

  • Compute attribute closure of X (denoted ) wrt F:
    • Set of all attributes A such that X A is in
    • There is a linear time algorithm to compute this.
  • Check if Y is in

• Does F = {A B, B C, C D E } imply A E?

  • i.e, is A E in the closure ? Equivalently, is E in ?

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