Efficient Digital Quadratic Unconstrained Binary Optimization Solvers for SAT Problems
Boolean satisfiability (SAT) is a propositional logic problem of determining whether an assignment of variables satisfies a Boolean formula. Many combinatorial optimization problems can be formulated in Boolean SAT logic -- either as k-SAT decision problems or Max k-SAT optimization problems, with c...
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Zusammenfassung: | Boolean satisfiability (SAT) is a propositional logic problem of determining
whether an assignment of variables satisfies a Boolean formula. Many
combinatorial optimization problems can be formulated in Boolean SAT logic --
either as k-SAT decision problems or Max k-SAT optimization problems, with
conflict-driven (CDCL) solvers being the most prominent. Despite their ability
to handle large instances, CDCL-based solvers have fundamental scalability
limitations. In light of this, we propose recently-developed quadratic
unconstrained binary optimization (QUBO) solvers as an alternative platform for
3-SAT problems. To utilize them, we implement a 2-step [3-SAT]-[Max
2-SAT]-[QUBO] conversion procedure and present a rigorous proof to explicitly
calculate the number of both satisfied and violated clauses of the original
3-SAT instance from the transformed Max 2-SAT formulation. We then demonstrate,
through numerical simulations on several benchmark instances, that digital QUBO
solvers can achieve state-of-the-art accuracy on 78-variable 3-SAT benchmark
problems. Our work facilitates the broader use of quantum annealers on noisy
intermediate-scale quantum (NISQ) devices, as well as their quantum-inspired
digital counterparts, for solving 3-SAT problems. |
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DOI: | 10.48550/arxiv.2408.03757 |