ON EQUIVALENCY REASONING FOR CONFLICT DRIVEN CLAUSE LEARNING SATISFIABILITY SOLVERS

Satisfiability problem or SAT is the problem of deciding whether a Boolean function evaluates to true for at least one of the assignments in its domain. The satisfiability problem is the first problem to be proved NP-complete. Therefore, the problems in NP can be encoded into SAT instances. Many hard real world problems can be solved when encoded efficiently into SAT instances. These facts give SAT an important place in both theoretical and practical computer science. In this thesis we address the problem of integrating a special class of equivalency reasoning techniques, the strongly connected components or SCC based reasoning, into the class of conflict driven clause learning or CDCL SAT solvers. Because of the complications that arise from integrating the equivalency reasoning in CDCL SAT solvers, to our knowledge, there has been no CDCL solver which has applied SCC based equivalency reasoning dynamically during the search. We propose a method to overcome these complications. The method is integrated into a prominent satisfiability solver: MiniSat. The equivalency enhanced MiniSat, Eq-MiniSat, is used to explore the advantages and disadvantages of the equivalency reasoning in conflict clause learning satisfiability solvers. Different implementation approaches for Eq-MiniSat are discussed. The experimental results on 16 families of instances shows that equivalency reasoning does not have noticeable effects for the instances in one family. The equivalency reasoning enables Eq-MiniSat to outperform MiniSat on eight classes of instances. For the remaining seven families, MiniSat outperforms Eq- MiniSat. The experimental results for random instances demonstrate that almost in all cases the number of branchings for Eq-Minisat is smaller than Minisat