DEPENDENCE STRUCTURE— DEPENDENCE AS A BINARY RELATION

Abstract

In systems theory, we often use the concept of dependence. There are several research to construct a unified framework for dependence. Mainly, the concept of dependence is defined with a dais of subsets, where the concept of algebraic closure systems is often used.

In this paper, we define dependence as a binary relation, which we call dependence structure, and develop a similar argument as for the dependence with a class of subsets. And we will clarify a relationship between dependence structure and the usual concept of dependence.

We also show what conditions assure the existence of a basis for a dependence structure.

The concept of functional dependence in database theory can be represented as a dependence structure and we will show that a key for a relational scheme is a basis for the dependence structure.

Keywords:

• Dependence structure
• dependence
• algebraic closure system
• basis
• minimal spanning set
• maximal independent set

Additional information

Notes on contributors

NAOKI SHIBA

Correponding author. 610. Olim Building, The Case School of Engineering Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 4416-7070, USA. Tel.: [phone]. Fax: [phone]. E_mail: naoki@me titech.ac.jp.