Abstract. In this paper, a new pre-processing step is proposed in the resolution of SAT instances, that recovers and exploits structural knowledge that is hidden in the CNF. It delivers an hybrid formula made of clauses together with a set of equations of the form y = f (x1, . . . , xn) where f is a standard connective operator among (∨, ∧, ⇔) and where y and xi are boolean variables of the initial SAT instance. This set of equations is then exploited to eliminate clauses and variables, while preserving satisfiability. These extraction and simplification techniques allowed us to implement a new SAT solver that proves to be the most efficient current one w.r.t. several important classes of instances.
In this paper a new approach for computing Strong Backdoor sets of boolean formula in conjunctive normal form (CNF) is proposed. It makes an original use of local search techniques for finding an assignment leading to a largest renamable Horn sub-formula of a given CNF. More precisely, at each step, preference is given to variables such that when assigned to the opposite value lead to the smallest number of remaining nonHorn clauses. Consequently, if no positive or non Horn clauses remain in the formula, our approach answer the satisfiability of the original formula; otherwise, a smallest non-Horn sub-formula is used to extract the set of variables (Strong Backdoor) such that when assigned leads to a tractable sub-formula. Branching on the variables of the Strong Backdoor set leads to significant improvements of Zchaff SAT solver with respect to many real worlds SAT instances.
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