One of the most important paradigm shifts in the use of SAT solvers for solving industrial
problems has been the introduction of clause learning. Clause learning entails adding a …

MaxSAT solving is becoming a competitive generic approach for solving combinatorial
optimization problems, partly due to the development of new solving techniques that have …

This chapter gives an overview of proof complexity and connections to SAT solving, focusing
on proof systems such as resolution, Nullstellensatz, polynomial calculus, and cutting planes …

SAT solving in large distributed environments has previously led to some famous results and
to impressive speedups for selected inputs. However, in terms of general-purpose SAT …

Maximum satisfiability (MaxSAT) is an optimization version of SAT that is solved by finding
an optimal truth assignment instead of just a satisfying one. In MaxSAT the objective function …

In recent years there has been an increasing interest in studying proof systems stronger than
Resolution, with the aim of building more efficient SAT solvers based on them. In defining …

Conflict-driven clause learning (CDCL) is at the core of the success of modern SAT solvers.
In terms of propositional proof complexity, CDCL has been shown as strong as general …

MaxSAT is a very popular language for discrete optimization with many domains of
application. While there has been a lot of progress in MaxSAT solvers during the last …

We study the MaxSAT Resolution (MaxRes) rule in the context of certifying unsatisfiability.
We show that it can be exponentially more powerful than tree-like resolution, and when …

Proof systems for SAT are unsound for MaxSAT because they preserve satisfiability but fail
to preserve the minimum number of unsatisfied clauses. Consequently, there has been a …