Journal of Mathematics and Statistics

SWITCHING-ALGEBRAIC ANALYSIS OF RELATIONAL DATABASES

Ali Muhammad Ali Rushdi and Omar Mohammed Ba-Rukab

DOI : 10.3844/jmssp.2014.231.243

Journal of Mathematics and Statistics

Volume 10, Issue 2

Pages 231-243

Abstract

There is an established equivalence between relational database Functional Dependencies (FDs) and a fragment of switching algebra that is built typically of Horn clauses. This equivalence pertains to both concepts and procedures of the FD relational database domain and the switching algebraic domain. This study is an exposition of the use of switching-algebraic tools in solving problems typically encountered in the analysis and design of relational databases. The switching-algebraic tools utilized include purely-algebraic techniques, purely-visual techniques employing the Karnaugh map and intermediary techniques employing the variable-entered Karnaugh map. The problems handled include; (a) the derivation of the closure of a Dependency Set (DS), (b) the derivation of the closure of a set of attributes, (c) the determination of all candidate keys and (d) the derivation of irredundant dependency sets equivalent to a given DS and consequently the determination of the minimal cover of such a set. A relatively large example illustrates the switching-algebraic approach and demonstrates its pedagogical and computational merits over the traditional approach.

Copyright

© 2014 Ali Muhammad Ali Rushdi and Omar Mohammed Ba-Rukab. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.