Dense Families and Key Functions of Database Relation Instances

In this paper dense families of database relations are introduced. We characterize dependencies and keys of relation instances in terms of dense families. Key functions are also introduced. They are isotone Boolean functions, which minimal true vectors are the characteristic vectors of the keys. We show that each dense family determines an isotone Boolean function which is the dual of the key function. We also show how to determine for a given relation r an r-dense family which size is at most m2 /2−m/2+1, where m is the number of tuples in r.

• Type: Conference
• Year: 2001
• Where: FCT
• Authors: Jouni Järvinen
• Keywords: Applied Computing, Dense Families, FCT 2001, Isotone Boolean Function, Key Function