Complexity of identification and dualization of positive Boolean functions
Information and Computation
On the complexity of dualization of monotone disjunctive normal forms
Journal of Algorithms
Asymptotic properties of keys and functional dependencies in random databases
Theoretical Computer Science - Special issue: database theory
Fundamentals of Database Systems
Fundamentals of Database Systems
Preimage Relations and Their Matrices
RSCTC '98 Proceedings of the First International Conference on Rough Sets and Current Trends in Computing
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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.