Lax Lean Archive

NP-hardness of SAT

Lax429075.SATHard · concepts/Lax429075/SATHard.lean · lax-429075

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    Natural Language Statement

    Lemma

    Every language in NP has a polynomial many-one reduction to the binary language of satisfiable CNF formulas.

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    8 concepts
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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

    Each proof establishes this claim relative to its assumptions.

    In the paper

    • page 3 of this submission's paper

    Lean source view on GitHub

    1import Lax429075.Satisfiability
    2import Lax429075.Reductions
    3
    4/-!
    5---
    6title: NP-hardness of SAT
    7type: lemma
    8---
    9Every language in NP has a polynomial many-one reduction to the binary
    10language of satisfiable CNF formulas.
    11-/
    12
    13namespace Lax429075.SATHard
    14
    15open Satisfiability Reductions Lax434930.PolynomialTime Lax434930.NondeterministicPolynomialTime
    16
    17axiom hardness (A : Language) : A ∈ NP → ManyOne A SAT
    18
    19end Lax429075.SATHard
    20
    Show Proof
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