On Irrelevant Literals in Pseudo-Boolean Constraint Learning
Résumé
Learning pseudo-Boolean (PB) constraints in PB solvers using the cutting planes proof system is a problem that is not as well understood as clause learning in conflict driven clause learning solvers.
In particular, it turns out that approaches based on generalized resolution may derive PB constraints containing irrelevant literals, i.e., literals whose assigned values (whatever they are) never change the truth value of the constraint.
This may happen even when starting from inputs without irrelevant literals.
We observe such situations empirically on benchmarks from the latest PB evaluation.
We perform an experiment exhibiting the negative impact of irrelevant literals on the runtime of solvers, by showing that their removal may be beneficial, in our case to Sat4j.