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On ‘Big’ Boolean-Equation Solving and Its Utility in Combinatorial Digital Design | Chapter 03 | Advances in Applied Science and Technology Vol. 2

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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