Mohamed Hesham Mohamed Emam Elhalaby <br/><br/>
On the weighted partial maximum satis ability problem /  
 دراسة بعض حالات مسألة التحقق الجزئي للصيغة البولياوية ذات الوزن الاكبر 
Mohamed Hesham Mohamed Emam Elhalaby ; Supervised L. F. Abdelal ,  Rasha Mohamed Shaheen 
 - Cairo :   Mohamed Hesham Mohamed Emam Elhalaby ,   2015 
 - 195 P. :   charts ;   25cm 
<br/><br/>Thesis (M.Sc.) - Cairo University - Faculty of Science - Department of Mathematics 
<br/><br/> This thesis is concerned with the Weighted Partial Maximum Satis-  ability problem (WPMax-SAT). Let z = zSzH be a Boolean formula such that zS =  and zH = ), . . . , (Cs+h, )}, Ci, (1  i  s + h) are clauses and wj, (1  j  s + h) (called weights) is either a natural number or . The WPMax-SAT problem for z is  nding an assignment that satis es all the hard clauses and maximizes the sum of the weights of the soft clauses. We dis- cuss four aspects of WPMax-SAT. The  rst is the computational complexity of the problem from the classical and the parametrized perspectives. Secondly, the two solving techniques of WPMax-SAT: branch and bound and SAT-based methods. Third, our experimental investigation on a number of selected solvers. Finally, the applica- tions of WPMax-SAT in real-life. 
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<br/><br/><label>Subjects--Index Terms: </label>Boolean formula Computational complexity  Satisfiability