Switching-Algebraic Analysis of Relational Databases

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.

Construction of General Subsumptive Solutions of Boolean Equations via Complete-Sum Derivation

“…The CS method for solving Boolean equations can be classified as an application of the Modern Syllogistic Method (MSM) (Blake, 1937;Brown, 1990;Gregg, 1998;Rushdi and Al-Shehri, 2002;Rushdi and Baz, 2007;Rushdi and Ba-Rukab, 2007;2008a;2008b;2009;2014). In this perspective, the equation f (X) 0 = can be viewed as a set of premises in a logic-deduction process, while the equation CS(f (X)) is thought of as a set of consequents in this deduction.…”