  CNF-based SAT and MaxSAT solvers are central to logic synthesis and
verification systems. The increasing popularity of these constraint problems in
electronic design automation encourages studies on different SAT problems and
their properties for further computational efficiency. There has been both
theoretical and practical success of modern Conflict-driven clause learning SAT
solvers, which allows solving very large industrial instances in a relatively
short amount of time. Recently, machine learning approaches provide a new
dimension to solving this challenging problem. Neural symbolic models could
serve as generic solvers that can be specialized for specific domains based on
data without any changes to the structure of the model. In this work, we
propose a one-shot model derived from the Transformer architecture to solve the
MaxSAT problem, which is the optimization version of SAT where the goal is to
satisfy the maximum number of clauses. Our model has a scale-free structure
which could process varying size of instances. We use meta-path and
self-attention mechanism to capture interactions among homogeneous nodes. We
adopt cross-attention mechanisms on the bipartite graph to capture interactions
among heterogeneous nodes. We further apply an iterative algorithm to our model
to satisfy additional clauses, enabling a solution approaching that of an
exact-SAT problem. The attention mechanisms leverage the parallelism for
speedup. Our evaluation indicates improved speedup compared to heuristic
approaches and improved completion rate compared to machine learning
approaches.
