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Lax307052.ConfigCount

Number of bounded configurations

concepts/Lax307052/ConfigCount.lean · lax-307052

proven

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    Lemma

    For input length nn and work bound ss, a machine with state set QQ and work alphabet Γ\Gamma has ∣Q∣(n+2)s∣Γ∣s|Q|(n+2)s|\Gamma|^s bounded configurations.

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    1import Lax307052.BoundedConfigurations
    2
    3/-!
    4---
    5title: Number of bounded configurations
    6type: lemma
    7---
    8For input length nn and work bound ss, a machine with state set QQ
    9and work alphabet Γ\Gamma has ∣Q∣(n+2)s∣Γ∣s|Q|(n+2)s|\Gamma|^s bounded configurations.
    10-/
    11
    12namespace Lax307052.ConfigCount
    13
    14open Lax434930.SpaceMachines BoundedConfigurations
    15
    16axiom count (M : Machine) (n s : ℕ) :
    17 Fintype.card (Config M n s) =
    18 Fintype.card M.Q * (n + 2) * s * Fintype.card M.Γ ^ s
    19
    20end Lax307052.ConfigCount
    21
    Show Proof

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