Synthesis Algorithm

compute a lossless transformation into a set of 3NF relation schemas using the Synthesis algorithm

Compute a Minimal Cover $F_{c}$ of original set of $F$
For each distinct left hand side $X$ in $F_{c}$ , let $Y$ be the union of all attributes $A$ such that $X \to A \in F_{c}$ . Form a relation schema $R_{X} = X \cup Y$
Let $K$ be any candidate key of the original schema. If no $R_{X}$ contain $K$ , add one more schema $R_{K} = K$
Eliminate any $R_{X}$ that is a strict subset of another schema

Result: A collection of relation schemas in 3NF that preservers FD's and guarantees a lossless join.