3 articles for “Boolean Equations”

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Research ArticleOpen accessPhrase in the titleCONSTRUCTION OF GENERAL SUBSUMPTIVE SOLUTIONS OF BOOLEAN EQUATIONS VIA COMPLETE-SUM DERIVATIONAli Muhammad Ali Rushdi, Hussain Mobarak AlbarakatiBoolean-equation solving permeates many diverse areas of modern science. To solve a system of Boolean equations, one usually combines them into an equivalent single Boolean equation {f(X) = 0} whose set of solutions is exactly the same as that of the original system of equations. One of the general classes of solutions for Boolean equations is the subsumptive general solution, … …Journal of Mathematics and Statistics, Vol. 10, Issue 2 · 13 Mar 2014 · 7,109 accessesView PDF Cite

Research ArticleOpen accessPhrase in the titleThe Inverse Problem for Boolean EquationsAli Muhammad Ali Rushdi, Hussain Mobarak AlbarakatiThe Forward Problem (FB) of Boolean equations consists of finding solutions of a system of Boolean equations, or equivalently, a single Boolean equation of the form f(X) = 0 where f(X): Bn → B and B is an arbitrary Boolean algebra. By contrast, the Inverse Problem (IB) of Boolean equations aims to reconstruct the equation f (X) = 0 given … …Journal of Computer Science, Vol. 8, Issue 12 · 3 Jan 2013 · 8,353 accessesView PDF Cite

Research ArticleOpen accessEvery word in the titleON REDUCED SCALAR EQUATIONS FOR SYNCHRONOUS BOOLEAN NETWORKSAli Muhammad Ali Rushdi, Adnan Ahmad AlsogatiA total description of a synchronous Boolean network is typically achieved by a matrix recurrence relation. A simpler alternative is to use a scalar equation which is a possibly nonlinear equation that involves two or more instances of a single scalar variable and some Boolean operator(s). Further simplification is possible in terms of a linear reduced scalar equation which is … …Journal of Mathematics and Statistics, Vol. 9, Issue 3 · 10 Sep 2013 · 6,665 accessesView PDF Cite