Existing methods provide varying algorithms for different types of Boolean satisfiability problems (SAT), lacking a general solution framework. Accordingly, this study proposes a unified framework DCSAT based on integer programming and reinforcement learning (RL) algorithm to solve different types of SAT problems such as MaxSAT, Weighted MaxSAT, PMS, WPMS. Specifically, we first construct a consolidated integer programming representation for four types of SAT problems by adjusting objective function coefficients. Secondly, we construct an appropriate reinforcement learning models based on the 0-1 integer programming for SAT problems. Based on the binary tree search structure, we apply the Monte Carlo tree search (MCTS) method on SAT problems. Finally, we prove that this method can find all optimal Boolean assignments based on Wiener-khinchin law of large Numbers. We experimentally verify that this paradigm can prune the unnecessary search space to find the optimal Boolean assignments for the problem. Furthermore, the proposed method can provide diverse labels for supervised learning methods for SAT problems.

We furnish solid evidence, both theoretical and empirical, towards the existence of a deterministic algorithm for random sparse $\#\Omega(\log n)$-SAT instances, which computes the exact counting of satisfying assignments in sub-exponential time. The algorithm uses a nice combinatorial property that every CNF formula has, which relates its number of unsatisfying assignments to the space of its monotone sub-formulae.