In computational complexity theory, a decision problem is NP-complete when it is both in NP and NP-hard. Although a solution to a NP-complete can be verified quickly, there is no known algorithm to solve it in polynomial time. There exists a method to reduce a SAT (Satifiability) problem to Subset Sum Problem (SSP) in the literature, however, it can only be applied to small or medium size problems. Our study is to find an efficient method to transform a SAT problem to a mixed integer linear programming problem in larger size. Observing the feature of variable-clauses constraints in SAT, we apply linear inequality model (LIM) to the problem and propose a method called LIMSAT. The new method can work efficiently for very large size problem with thousands of variables and clauses in SAT tested using up-to-date benchmarks.
With the increasing performance of SAT solvers, a lot of distinct problems, coming from very disparate fields, are added to the pool of Application problems, regularly used to rank solvers. These problems are also widely used to measure the positive impact of any new idea. We show in this paper that many of them have extreme behaviors that any SAT solvers must cope with. We show that, by adding a few, simple, human-readable, indicators, we can let Glucose choose between four strategies to show important improvements on the set of the hardest problems from all the competitions between 2002 and 2013 included. Moreover, once the SAT solver has been specialized, we show that a new restart polarity policy can improve even more the results. Without the first specialization step mentioned above, this new and effective policy would have been jugged inefficient. Our final Glucose is capable of solving (20 , ) more problems than the original one, while speeding up also UNSAT answers.