Thinking Out of the Box: Hybrid SAT Solving by Unconstrained Continuous Optimization
This addresses a bottleneck in combinatorial optimization and verification for applications requiring hybrid constraints, though it is incremental as it builds on existing polynomial representations.
The paper tackled the problem of solving hybrid SAT problems with non-CNF constraints by proposing unconstrained continuous optimization formulations using penalty terms, and demonstrated empirically that unconstrained optimizers like Adam can enhance SAT solving on hybrid benchmarks.
The Boolean satisfiability (SAT) problem lies at the core of many applications in combinatorial optimization, software verification, cryptography, and machine learning. While state-of-the-art solvers have demonstrated high efficiency in handling conjunctive normal form (CNF) formulas, numerous applications require non-CNF (hybrid) constraints, such as XOR, cardinality, and Not-All-Equal constraints. Recent work leverages polynomial representations to represent such hybrid constraints, but it relies on box constraints that can limit the use of powerful unconstrained optimizers. In this paper, we propose unconstrained continuous optimization formulations for hybrid SAT solving by penalty terms. We provide theoretical insights into when these penalty terms are necessary and demonstrate empirically that unconstrained optimizers (e.g., Adam) can enhance SAT solving on hybrid benchmarks. Our results highlight the potential of combining continuous optimization and machine-learning-based methods for effective hybrid SAT solving.