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Post's correspondence problem is RE-complete

Lax624099.PcpREComplete · concepts/Lax624099/PcpREComplete.lean · lax-624099

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    Natural Language Statement

    Theorem

    PCP is RE-complete: a match is recognized by guessing it in existential second-order logic with value invention, and the halting problem reduces to PCP by an ordered first-order reduction, the computation-history dominoes.

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

    Each proof establishes this claim relative to its assumptions.

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    1import Lax904597.Problems
    2import Lax904597.Interpretations
    3import Lax904597.Relativized
    4import Lax904597.Classes
    5import Lax624099.Problems
    6import Lax624099.ValueInvention
    7import Lax624099.ClassRE
    8import Lax624099.FiniteSatisfiability
    9import Lax624099.Halting
    10import Lax624099.CodeHalting
    11import Lax624099.PostCorrespondence
    12import Lax624099.ConcreteInstances
    13import Lax904597.Machines
    14
    15/-!
    16---
    17title: Post's correspondence problem is RE-complete
    18type: theorem
    19---
    20PCP is RE-complete: a match is recognized by guessing it in existential
    21second-order logic with value invention, and the halting problem reduces to
    22PCP by an ordered first-order reduction, the computation-history dominoes.
    23-/
    24
    25namespace Lax624099.PcpREComplete
    26
    27open FirstOrder FirstOrder.Language
    28open Lax904597.Problems Lax904597.Interpretations Lax904597.Relativized Lax904597.Classes
    29open Lax904597.Machines Lax624099.Problems Lax624099.ValueInvention Lax624099.ClassRE
    30open Lax624099.FiniteSatisfiability
    31open Lax624099.Halting Lax624099.CodeHalting Lax624099.PostCorrespondence
    32open Lax624099.ConcreteInstances
    33
    34/-- PCP is RE-complete. -/
    35axiom pcp_RE_complete : RE.Complete PCP
    36
    37end Lax624099.PcpREComplete
    38
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