This chapter considers the problem of solving a system of Boolean equations over a finite (atomic) Boolean algebra other than the two-valued one. A prominent “misnomer” in mathematical and engineering circles is the term ‘Boolean algebra’. This term is widely used to refer to switching algebra, which is just one particular case of a ‘Boolean algebra’ that has 0 generators, 1 atom and two elements belonging to B={0,1}.The chapter outlines classical and novel direct methods for deriving the general parametric solution of such a system and for listing all its particular solutions. A detailed example over Bis used to illustrate these two methods as well as a third method that starts by deriving the subsumptive solution first. The example demonstrates how the consistency condition forces a collapse of the underlying Boolean algebra to a subalgebra, and also how to list a huge number of particular solutions in a very compact space. Subsequently, the chapter proposes some potential applications for the techniques of Boolean-equation solving. These techniques are very promising as useful extensions of classical techniques based on two-valued Boolean algebra.
Author(s) Details
Ali Muhammad Ali Rushdi
Department of Electrical and Computer Engineering, King Abdulaziz University, P.O.Box 80204, Jeddah 21589, Saudi Arabia.
Sultan Sameer Zagzoog
Department of Electrical and Computer Engineering, King Abdulaziz University, P.O.Box 80204, Jeddah 21589, Saudi Arabia.
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