Asymptotic properties of keys and functional dependencies in random databases
Theoretical Computer Science - Special issue: database theory
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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 H2 (A→b) is an entropy like functional of the probability distribution of the data.