Thinking Out of the Box: Hybrid SAT Solving by Unconstrained Continuous Optimization

TL;DR

This paper introduces a novel approach to hybrid SAT solving using unconstrained continuous optimization with penalty terms, enabling the use of optimizers like Adam for better performance on complex hybrid constraints.

Contribution

It presents the first unconstrained continuous optimization formulations for hybrid SAT solving, expanding the capabilities of existing polynomial-based methods.

Findings

Unconstrained optimizers improve hybrid SAT solving performance.

Penalty terms are crucial for effective unconstrained formulations.

Empirical results show enhanced solving on hybrid benchmarks.

Abstract

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.