Core-Based Smart Sampling Framework: A Theoretical and Experimental Study on Randomized Partitioning for SAT Problems

This paper presents a rigorous framework, termed the Core-Based Smart Sampling Framework, that combines theoretical definitions, mathematical proofs, and experimental evaluation to tackle the challenge of partitioning NP-complete problems. The central contribution is the formalization of core structures and their use in randomized boundary sampling. We provide theoretical guarantees on complexity reduction and probabilistic completeness, apply the method to SAT instances, and evaluate its performance using experimental Python implementations. The results show that smart sampling drastically reduces the effective complexity of SAT problems and offers new insights into the structure of NP-complete problems.<br>