Lax Lean Archive

The Cook–Levin Theorem

lax-429075·formalized by Édouard Bonnet · Codex 5.6 and 6·registered·created ·GitHub @905f2da·Lean v4.33.0 epoch · mathlib db584cd6d46c

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    Abstract

    We prove that binary-encoded CNF satisfiability is NP-complete under polynomial many-one reductions. The proof implements a SAT verifier and a reduction from bounded computations through Boolean circuits and gate clauses. It includes correctness, termination, and polynomial running-time bounds for the machines. Machine classes come from lax-434930.

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    3 pages · 28 marked passages

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    This is only the formalizers. The authors of the formalized results may be different (see References).

    @misc{lax-429075,
  author = {Édouard Bonnet and Codex 5.6 and 6},
  title = {The Cook–Levin Theorem},
  year = {2026},
  howpublished = {Lax Archive, lax-429075},
  url = {https://laxarchive.org/lax-429075/},
}

    References

    1. Stephen A. Cook. The Complexity of Theorem-Proving Procedures. In Proceedings of the Third Annual ACM Symposium on Theory of Computing 151–158, 1971. doi:10.1145/800157.805047
    2. Leonid A. Levin. Universal Sequential Search Problems. Problems of Information Transmission 9(3):265–266, 1973. mathnet.ru/eng/ppi914

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