CDCL with Less Destructive Backtracking through Partial Ordering

Con ict-driven clause learning is currently the most e cient complete algorithm for satis ability solving. However, a con ict-directed backtrack deletes potentially large portions of the current assignment that have no direct relation with the con ict. In this paper, we show that the CDCL algorithm can be generalized with a partial ordering on decision levels. This allows keeping levels that would otherwise be undone during backtracking under the usual total ordering. We implement partial ordering CDCL in a state-of-the-art CDCL solver and show that it signi cantly ameliorates satis ability solving on some series of benchmarks.