database - Given a relation with FDs, compute the closure of set of attributes -


consider relation schema r = abcdg following functional dependencies (fd) 

ab  -> c c   -> bc  -> d acd -> d d   -> eg  -> c cg  -> bd ce  -> ag

compute closure of bd , ca.

how can find them?

the closure of set of functional dependencies, f, means functional dependencies logically implied f. example, given

  • bc -> d, and
  • d -> eg

we can apply armstrong's axioms derive

  • d -> e,
  • d -> g,
  • bc -> e,
  • bc -> g,

and on.

when you've derived every fd implied f, have closure of f respect r. in case, want derive every fd logically implied bd , ca.

as far know, every textbook on relational database theory includes 1 or more algorithms compute closure of set of functional dependencies. best bet follow 1 of algorithms in textbook, if have one.


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