Lax Lean Archive

Single-tape characterization of P

Lax434930.ModelEquivalence · concepts/Lax434930/ModelEquivalence.lean · lax-434930

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    Natural Language Statement

    Lemma

    The elementary single-tape and stack-machine definitions of P\mathrm{P} coincide. Both simulations include polynomial bounds for input conversion, execution, and final output conversion.

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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 Lax434930.MachineModels
    2
    3/-!
    4---
    5title: Single-tape characterization of P
    6type: lemma
    7---
    8The elementary single-tape and stack-machine definitions of P\mathrm{P}
    9coincide. Both simulations include polynomial bounds for input conversion,
    10execution, and final output conversion.
    11-/
    12
    13namespace Lax434930.ModelEquivalence
    14
    15open PolynomialTime MachineModels
    16
    17/-- The elementary single-tape and stack definitions give the same class P. -/
    18axiom singleTapeP_eq_P : SingleTapeP = P
    19
    20end Lax434930.ModelEquivalence
    21
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