Focusing with conflicts
Lemma: Let A2 be an (eventual) successor of A1 such that A1 contains a conflict N, but A2 does not. Then there exists an immediate successor A3 of A1 that doesn’t contain N such that A2 is an (eventual) successor of A3.
If an assignment A1 is infeasible and contains a conflict N, then we need only generate those immediate successors of A1 that don’t contain N
- the lemma ensures that completeness is preserved
- the smaller the conflict, the fewer the immediate successors