On the power of clause-learning SAT solvers as resolution engines

摘要

In this work, we improve on existing results on the relationship between proof systems obtained from conflict-driven clause-learning SAT solvers and general resolution. Previous contributions such as those by Beame et al. (2004), Hertel et al. (2008), and Buss et al. (2008) demonstrated that variations on conflict-driven clause-learning SAT solvers corresponded to proof systems as powerful as general resolution. However, the models used in these studies required either an extra degree of non-determinism or a preprocessing step that is not utilized by state-of-the-art SAT solvers in practice. In this paper, we prove that conflict-driven clause-learning SAT solvers yield proof systems that indeed p-simulate general resolution without the need for any additional techniques. Moreover, we show that our result can be generalized to certain other practical variations of the solvers, which are based on different learning schemes and restart policies.