Abstract
We introduce the notion of entropy for a set of attributes of a table in a relational database starting from the notion of entropy for finite functions. We examine the connections that exist between conditional entropies of attribute sets and lossy decompositions of tables and explore the properties of the entropy of sets of attributes regarded as an outer measure on the set of subsets of a heading of a table. Finally, we suggest a generalization of functional dependencies based on conditional entropy.
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References
K. T. Cheng, V. Agrawal, An entropy measure of the complexity of multi-output Boolean function, Proc. of the 27th Design Automation Conference, 1990, 302–305.
V. Cheushev, V. Shmerko, D. A. Simovici, S. Yanushkevich, Functional entropy and decision trees, Proc. ISMVL’98, 1998, 257–262.
P. A. Fejer, D. A. Simovici, Mathematical Foundations of Computer Science, vol. I, Springer-Verlag, New York, 1991.
C. H. Hwang and A. C. H. Wu, An entropy measure for power estimation of Boolean function, Proc. of Asia and South Pacific Design Automation Conference (ASP-DAC), 1997, 101–106.
S. Jaroszewicz, D. A. Simovici, On axiomatization of conditional entropy of functions between finite sets, Proc. of the 29th International Symposium for Multiple-Valued Logic, Freiburg, May 1999, to appear.
A. Lloris-Ruiz, J. F. Gomez-Lopera, R. Roman-Roldan, Entropic minimization of multiple-valued logic functions, Proc. ISMVL’93, 1993, 24–28.
A. M. Mathai, P. N. Rathie, Basic Concepts in Information Theory and Statistics — Axiomatic Foundations and Applications, Halsted Press, John Wiley & Sons, 1975.
D. A. Simovici, C. Reischer, On functional entropy, Proc. of the 23rd International Symposium for Multiple-Valued Logic, 1993, 100–104.
D. A. Simovici, R. L. Tenney, Relational Database Systems, Academic Press, New York, 1995.
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© 2000 Springer-Verlag London Limited
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Simovici, D.A., Jaroszewicz, S. (2000). On Information-Theoretical Aspects of Relational Databases. In: Finite Versus Infinite. Discrete Mathematics and Theoretical Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-0751-4_20
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DOI: https://doi.org/10.1007/978-1-4471-0751-4_20
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