Random Databases with Correlated Data

Abstract

A model of random databases is given, with arbitrary correlations among the data of one individual. This is given by a joint distribution function. The individuals are chosen independently, their number m is considered to be (approximately) known. The probability of the event that a given functional dependency A → b holds (A is a set of attributes, b is an attribute) is determined in a limiting sense. This probability is small if m is much larger than $2^{H_2(A\rightarrow b)/2}$ and is large if m is much smaller than $2^{H_2(A\rightarrow b)/2}$ where H ₂(A → b) is an entropy like functional of the probability distribution of the data.