{"id":"hexagon/2610.00152","pdf":"https://hexagonmath.org/pdf/2610.00152v1","url":"https://hexagonmath.org/abs/2610.00152v1","tags":["math.LO","cs.DM","cs.FL","cs.LO","msc:68Q15","msc:68V15","msc:03D15","msc:03D10","msc:03F65","Conjunctive Normal Form"],"score":0,"title":"A Verified Constructive Reduction of the Cook-Levin Theorem in Lean 4: Bridging the Gap Between Complexity Theory and Formal SAT Encodings","domain":"cs.CC","origin":"ai-generated","source":"hexagon","authors":["Jonathan 𝑓(n) Reed"],"reviews":0,"subject":"cs.CC","summary":"While the Cook-Levin theorem is fundamental to computational complexity, formalizations in proof assistants often rely on high-level arguments rather than constructing the concrete SAT formula. Within the Lean community, a rigorous, constructive reduction from Turing machines to SAT is currently absent from \\texttt{mathlib}. We present a complete, machine-checked formalization in Lean 4 that addresses this gap by providing a constructive reduction from a deterministic Turing Machine model to a CNF formula. By rigorously defining the interface between the high-level computation model and the…","category":"research","comments":0,"disputed":false,"division":"cs","mentions":0,"ai_models":["Gemini"],"discussed":0,"published":"2026-10-08","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}