# Decisional BCNF (BCNF Decomposition)

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## Description

Decisional BCNF is the problem of deciding whether or not a relation schema can be turned into Boyce-Codd normal form (BCNF).

A relation schema $R$ is in Boyce Codd Normal Form (abbr. BCNF) if for all non-trivial FDs $X \rightarrow Y$ in $F^+$, $X$ is a superkey. In extending this notion to database schemas, we must be conscious of the UR-assumption. We say that $R_i = <ATTR_i,F_i>$ is in BCNF if the schema $<ATTR_i, F^+(ATTR_i)>$ is in BCNF, and $D$ is in BCNF if each $R_i$ is.

## Related Problems

Related: BCNF Decomposition

## Parameters

$n$: size of database?

$k$: number of functional dependencies

## Table of Algorithms

Name | Year | Time | Space | Approximation Factor | Model | Reference |
---|---|---|---|---|---|---|

Liu | 1992 | $O(kn^{2})$ | $O(n)$ | Exact | Deterministic | Time |