# Max SAT Problem

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Introduction: Motivation: Boolean Satisfiability (SAT) problems take a great interest in mathematical logic and computing theories. The importance of this problem lies in its representation of many problems in different areas such as planning, scheduling, software testing and other areas. SAT solver solves SAT problems, but there is another solver that solves these problems which is called Partial MaxSAT (PMSAT) solver. PMSAT is considered to be an improvement of SAT solver which is distinguished from SAT solver by its flexibility in solving problems. Therefore, the authors are interested in solving curriculum course timetabling problem by using PMSAT solver and measure its effectiveness in solving this problem. Overview of SAT, PMSAT and…show more content…
SAT problem concentrates on hard constraints, but not all problems require hard constrains therefor SAT problem has many types like MaxSAT and PMSAT which are softer than SAT on constraints. The Max-SAT problem for a CNF formula φ is to find a model that maximizes the number of satisfied clauses in φ. The PMSAT is an extension of Max SAT .It is better for solving NP-hard problems which used to find a model for the hard clauses that maximizes the number of satisfied soft [3]. Course Timetabling (CTT) problem consists of weekly scheduling of lectures [4]. Every teacher can teach one course at a time, and every room contains one course at a time, therefor must satisfy multiple constraints and solve the conflict [5]. If a conflict of courses according to the curricula of university and not based on enrollment of data we called curriculum course timetabling problem. We apply PMSAT for handling the CCTT…show more content…
That solved just as hard and ignore the soft [8]. Fabio De Cesco, Luca Di Gaspero and Andrea Schaerf [9] in 2010 proposed a set of formulations for the Curriculum-Based Course Timetabling problem, to encouraging researchers to reduce" their specific problems to one of them, that helping to compare and assess their results. Nelson Rangel-Valdez, Jose Torres-Jimenez, Jorge Omar Jasso-Luna and Mario Humberto Rodriguez-Chavez1 in 2013 used a SAT model to solved special case of CCTT problem. which includes the constraint teacher cannot teach more than one course in the same curriculum ,reduces the time to construct the schedules from two weeks to minutes it also must satisfies the 3 hard constraints, and the 2 soft constraint. The result was solution all the special case [10]. Esraa Al-Otaibi, Muneera Al-Saeed and Wejdan Al-Jarallah in 2014 used a genetic algorithm to find all possible alternative schedules for the timetables and doing application according to registration's criteria of IMAMU. They construct schedules which contain hard constrain and not Add soft constrain to GA to increase the students