Algebraic Methods Versus Map Methods Of Solving Boolean Equations

Using variable-entered Karnaugh maps to produce compact parametric general solutions of Boolean equations

“…It also predicts the correct number of particular solutions of a Boolean equation, and produces a comprehensive list of particular solutions. The concepts and method developed herein can be utilized in various application areas of Boolean equations [4,6,7,11,15,18,19,23,24,30,31]. In particular, an automated version of the present Boolean-equation solver can be applied in the simulation of gate-level logic.…”

“…Various subsumptive solutions for Equation (5) have been repeatedly produced by Brown [6,7], Rushdi [23,24] and Rudeanu [19]. However, no attempt (to the best of our knowledge) has been made to produce a parametric solution for it.…”

[Technical Note] Purely-Algebraic versus VEKM Methods for Solving Big Boolean Equations

“…There are two prominent classes of methods used in the manual solution of big Boolean equations, namely, the class of purely-algebraic methods and the class of methods utilizing the variable-entered Karnaugh map (VEKM). This note compares the competitiveness of these two classes of methods, and sets the record straight by showing that the downgrading of VEKM methods in [1] is unjustified and inaccurate. The importance of this note is that it offers decisive facts that oppose opinions set forth by Professor Sergiu Rudeanu, who is widely and undisputedly recognized in pertinent circles as the father of modern Boolean equations.…”

“…Rudeanu states in [2] and reiterates in Ref. [1,3] that 'the algebraic theory of Boolean equations is very strong and provides various efficient methods for solving them.' For him, the '[map] procedures are, in fact, nothing but practical ways of organizing the [algebraic] methods,' [2] , and 'the map methods do not take advantage of the results provided by the algebraic theory, and besides, are limited to the case of the twoelement …or a finite Boolean algebra.'…”

“…To support his point, he resumed in Ref. [1] an equation solved in Ref. [4,5] by what he calls a tabular method, solved it algebraically, and recovered the compact solution in Ref.…”