In this paper we prove an exponential separation between two very similar and natural SAT encodings for the same problem, thereby showing that researchers must be careful when designing encodings, lest they accidentally introduce complexity into the problem being studied. This result provides a formal explanation for empirical results showing that the encoding of a problem can dramatically affe...

Max-SAT is the problem of finding an assignment minimizing the number of unsatisfied clauses of a given CNF formula. We propose a resolution-like calculus for Max-SAT and prove its soundness and completeness. We also prove the completeness of some refinements of this calculus. From the completeness proof we derive an exact algorithm for Max-SAT and a time upper bound.

This paper proposes an encoding a background-implying problem in attribute exploration of manyvalued context into a SAT problem. A background-implying problem is whether an attribute implication is implied by some other attribute implications and is also compatible with background knowledge. In the case of manyvalued context, the background knowledge will be its scales which are also formal con...

A recent success of SAT solving has been the solution of the boolean Pythagorean Triples problem [Heule et al., 2016], delivering the largest proof yet, of 200 terabytes in size. We present this and the underlying paradigm Cube-and-Conquer, a powerful general method to solve big SAT problems, based on integrating the “old” and “new” methods of SAT solving.