On Armstrong relations for strong dependencies

Abstract

The strong dependency has been introduced and axiomatized in [2], [3], [4], [5]. The aim of this paper is to investigate on Armstrong relations for strong dependencies. We give a necessary and sufficient condition for an abitrary relation to be Armstrong relation of a given strong scheme. We also give an effective algorithm finding a relation r such that r is Armstrong relation of a given strong scheme G = (U,S) (i.e. Sr = S+, where Sr is a full family of strong dependencies of r, and S+ is a set of all strong dependencies that can be derived from S by the system of axioms). We estimate this algorithm. We show that the time complexity of this algorithm is polynomial in |U| and |S|.