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Boyce-Codd normal form (BCNF) Kai Zhu CS157B Professor: Dr. Lee

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Functional dependency Given a relation R, a set of attributes X in R is said to functionally determine another attribute Y, also in R, if and only if each X value is associated with precisely one Y value. (written X → Y)

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Normalization Normalization is the process of efficiently organizing data in a database Purpose: 1. Eliminate redundant data 2. Ensure data dependencies make sense

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1NF Table faithfully represents a relation and has no repeating groups

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non-1NF 1NF

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2NF A 1NF table is in 2NF if and only if none of its non-prime attributes are functionally dependent on a subset of a candidate key. (A non-prime attribute is one that does not belong to any candidate key.)

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An example of a 1NF table that does not meet 2NF is:

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Candidate key: {Employee, Skill} The remaining attribute, Current Work Location, is dependent on only part of the candidate key, namely Employee. Therefore the table is not in 2NF.

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3NF A 2NF table is in 3NF if every non-prime attribute of R is non-transitively dependent (i.e. directly dependent) on every key of R.

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An example of a 2NF table that fails to meet the requirements of 3NF is: Candidate key: {Tournament, Year}

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It is not 3NF because the non-prime attribute Winner Date of Birth is transitively dependent on the candidate key {Tournament, Year} via the non- prime attribute Winner.

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Trivial functional dependency A functional dependency FD: X → Y is called trivial if Y is a subset of X.

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BCNF Boyce-Codd normal form (or BCNF) is a normal form used in database normalization. A table is in BCNF if and only if for every one of its non-trivial functional dependencies X → Y, X is a superkey—that is, X is either a candidate key or a superset thereof. (Y is not included in X)

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Consider the following non-BCNF table: The candidate keys of the table are: {Person, Shop Type} {Person, Nearest Shop}

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It is 3NF, WHY? Recall 3NF prohibits transitive functional dependencies of non-prime attributes on candidate keys. In relation “Nearest shop” table, there are no non-prime attributes: that is, all attributes belong to candidate keys. Therefore the table adheres to both 2NF and 3NF.

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Why it is not BCNF? The table does not adhere to BCNF because of the dependency Nearest shop → Shop Type, in which the determining attribute (Nearest shop ) is neither a candidate key nor a superset of a candidate key.

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What we can do if we need a relation to be BCNF?

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Normalizing…

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After normalization Candidate keys are {person, shop} and{shop},respectively.

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Thank you

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Normal Forms 1NF – A table that qualifies as a relation is in 1NF. (Back)(Back) 2NF – A relation is in 2NF if all of its nonkey attributes are dependent.

Normal Forms 1NF – A table that qualifies as a relation is in 1NF. (Back)(Back) 2NF – A relation is in 2NF if all of its nonkey attributes are dependent.

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