Conjunctive query evaluation is NP-complete

Lax420092.EvaluationNPComplete · concepts/Lax420092/EvaluationNPComplete.lean · lax-420092

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    Natural Language Statement

    Theorem

    Boolean conjunctive query evaluation, in combined complexity, is NP-complete in the sense of the NP core: it is definable in existential second-order logic, guessing the valuation, and 3-colorability reduces to it by a quantifier-free first-order reduction, the query of a graph being evaluated in the triangle. This is the evaluation half of Chandra and Merlin (1977).

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

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    Lean source view on GitHub

    1import Lax904597.Problems
    2import Lax904597.Interpretations
    3import Lax904597.Classes
    4import Lax799700.Problems
    5import Lax420092.QueryDatabases
    6import Lax420092.Evaluation
    7import Lax420092.QueryPairs
    8import Lax420092.PackagedInstances
    9
    10/-!
    11---
    12title: Conjunctive query evaluation is NP-complete
    13type: theorem
    14---
    15Boolean conjunctive query evaluation, in combined complexity, is NP-complete
    16in the sense of the NP core: it is definable in existential second-order
    17logic, guessing the valuation, and 3-colorability reduces to it by a
    18quantifier-free first-order reduction, the query of a graph being evaluated
    19in the triangle. This is the evaluation half of Chandra and Merlin (1977).
    20-/
    21
    22namespace Lax420092.EvaluationNPComplete
    23
    24open FirstOrder FirstOrder.Language
    25open Lax904597.Problems Lax904597.Interpretations Lax904597.Classes Lax799700.Problems
    26open Lax420092.QueryDatabases Lax420092.Evaluation Lax420092.QueryPairs Lax420092.PackagedInstances
    27
    28/-- CQEval is NP-complete. -/
    29axiom cqEval_NP_complete : NP.Complete CQEval
    30
    31end Lax420092.EvaluationNPComplete
    32
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