Research ArticleOpen accessIn the author namesSWITCHING-ALGEBRAIC ANALYSIS OF RELATIONAL DATABASESAli Muhammad Ali Rushdi, Omar Mohammed Ba-RukabThere 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 … …Journal of Mathematics and Statistics, Vol. 10, Issue 2 · 18 Apr 2014 · 6,705 accessesView PDFCite
Research ArticleOpen accessIn the author namesCONSTRUCTION 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 PDFCite
Research ArticleOpen accessIn the author namesON 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 PDFCite
Research ArticleOpen accessIn the author namesON SELF-INVERSE BINARY MATRICES OVER THE BINARY GALOIS FIELDAli Muhammad Ali Rushdi, Fares Ahmad Muhammad GhalebAn important class of square binary matrices over the simplest finite or Galois Field GF(2) is the class of involutory or Self-Inverse (SI) matrices. These matrices are of significant utility in prominent engineering applications such as the study of the Preparata Transformation or the analysis of synchronous Boolean Networks. Therefore, it is essential to devise appropriate methods, not only for … …Journal of Mathematics and Statistics, Vol. 9, Issue 3 · 4 Sep 2013 · 7,248 accessesView PDFCite
Research ArticleOpen accessIn the author namesThe 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 PDFCite
Research ArticleOpen accessIn the author namesPowerful Features of the Modern Syllogistic Method of Propositional LogicAli Muhammad Rushdi, Omar Mohammed Ba-RukabIn traditional propositional logic, many replacement and inference rules were involved to ascertain if the truth of several antecedents implied the truth of a particular consequent. This research described a powerful technique called the Modern Syllogistic Method (MSM), which ferreted out from a set of premises all that can be concluded from it and casted the resulting conclusions in the … …Journal of Mathematics and Statistics, Vol. 4, Issue 3 · 30 Sep 2008 · 7,108 accessesView PDFCite
Research ArticleOpen accessIn the author namesCost Elasticities of Reliability and MTTF for k-out-of-n SystemsAli Muhammad Rushdi, Abdulaziz Efain AlsulamiThe application of the concept of cost elasticity of reliability was extended from the parallel system to the partially redundant or k-out-of-n:G(F) system (or k-out-of-n system, for short). An expression for the cost elasticity of reliability was derived for a general k-out-of-n system. The expression yielded acceptable results for a wide range of values for k, n, and component reliability. … …Journal of Mathematics and Statistics, Vol. 3, Issue 3 · 30 Sep 2007 · 7,295 accessesView PDFCite