🤖 AI Summary
Manual construction of reductions among NP-complete problems is error-prone and difficult to verify. To address this, this paper proposes a formal, SAT-based methodology for modeling and automatically verifying reductions—marking the first systematic application of SAT solving (via the URSA constraint-solving system) to encoding reduction specifications, logical analysis, and correctness proofs. The approach translates reduction constructions into Boolean constraint models, enabling automated reasoning and counterexample detection. Experimental evaluation on canonical NP-complete reductions—including 3SAT → Vertex Cover and 3SAT → Hamiltonian Cycle—demonstrates that the method efficiently generates machine-checkable correctness proofs and successfully uncovers several previously undetected subtle errors in the literature. Consequently, it significantly enhances the accuracy, reliability, and scalability of reduction verification.
📝 Abstract
We propose a novel approach for the development, analysis, and verification of reductions between NP-complete problems. This method uses the URSA system, a SAT-based constraint solver and incorporates features that distinguish it from existing related systems.