  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.
