SZTAKI Közlemények 34. (1986)

Ho Thuan: Some invariants of covers for functional dependencies

MTA SZTAKI Közlemények 34/1986 pp.151-162 SOME INVARIANTS OF COVERS FOR FUNCTIONAL DEPENDENCIES Ho Thuan MTA SZTAKI ABSTRACT The nonredundant and minimum covers have been investigated by different approaches in Cl], L21, and several useful pro­perties of them have been proved and used in various problems in the logical design of databases. But few attention is paid to the study of invariants concerning the attribute sets of the left and right sides of these covers. In this paper, we prove some additional invariants for covers and nonredundant covers. Most of these results have been presented in C 3 D but the proofs given there are too long and the required assumptions are too strict. We will provide them in a weakened form and with much shorter proofs. SI. INTRODUCTION In most studies concerning covers for functional dependencies, we usually start from a set F of FDs on Q={A1,A2,...,An> F = {L. -V R. ! i = 1 ,k L., R. C 0} l l 1 l ' l — and try to find a shorter representation for F, i.e. a new set F' of FDs with either a fewer number of FDs or a less total

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