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Exact Max-SAT solvers, compared with SAT solvers, apply little inference at each node of the proof tree. Commonly used SAT inference rules like unit propagation produce a simplified formula that preserves satisfiability but, unfortunately, solving the Max-SAT problem for the simplified formula is not equivalent to solving it for the original formula. In(More)
The Pseudo-Boolean Optimization (PBO) and Maximum Satisfiability (MaxSAT) problems are natural optimization extensions of Boolean Satisfiability (SAT). In the recent past, different algorithms have been proposed for PBO and for MaxSAT, despite the existence of straightforward mappings from PBO to MaxSAT and vice-versa. This papers proposes Weighted Boolean(More)
Many lower bound computation methods for branch and bound Max-SAT solvers can be explained as procedures that search for disjoint inconsistent subformulas in the Max-SAT instance under consideration. The difference among them is the technique used to detect inconsistencies. In this paper, we define five new lower bound computation methods: two of them are(More)
We investigate the role of cycles structures (i.e., subsets of clauses of the form ¯ l1 ∨ l2, ¯ l1 ∨ l3, ¯ l2 ∨ ¯ l3) in the quality of the lower bound (LB) of modern MaxSAT solvers. Given a cycle structure, we have two options: (i) use the cycle structure just to detect inconsistent subformulas in the underestimation component, and (ii) replace the cycle(More)
Maximum Satisfiability (MaxSAT) is an optimization version of SAT, and many real world applications can be naturally encoded as such. Solving MaxSAT is an important problem from both a theoretical and a practical point of view. In recent years, there has been considerable interest in developing efficient algorithms and several families of algorithms have(More)
We present a new branch and bound algorithm for weighted Max-SAT, called Lazy, which incorporates original data structures and inference rules, as well as a lower bound of better quality. We provide experimental evidence that our solver is very competitive and outperforms some of the best performing Max-SAT and weighted MaxSAT solvers on a wide range of(More)
The lower bound (LB) implemented in branch and bound MaxSAT solvers is decisive for obtaining a competitive solver. In modern solvers like MaxSatz and MiniMaxSat, the LB relies on the cooperation of the underestimation and inference components. Actually, the underestimation component of some solvers guides the application of the inference component when a(More)