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Lax307052.BoundedConfigurations

Bounded machine configurations

concepts/Lax307052/BoundedConfigurations.lean · lax-307052

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    Definition

    A configuration using at most ss work cells consists of a control state, an input-head position, a work-head position, and ss work symbols. Cells beyond this prefix are blank.

    Lean source view on GitHub

    1import Lax434930.SpaceMachines
    2import Mathlib.Data.Fintype.Pi
    3
    4/-!
    5---
    6title: Bounded machine configurations
    7type: definition
    8---
    9A configuration using at most ss work cells consists of a control state,
    10an input-head position, a work-head position, and ss work symbols.
    11Cells beyond this prefix are blank.
    12-/
    13
    14namespace Lax307052.BoundedConfigurations
    15
    16open Lax434930.SpaceMachines
    17
    18structure Config (M : Machine) (n s : ℕ) where
    19 state : M.Q
    20 inputHead : Fin (n + 2)
    21 workHead : Fin s
    22 tape : Fin s → M.Γ
    23 deriving Fintype
    24
    25def expand {M : Machine} {n s : ℕ} (c : Config M n s) : M.Config :=
    26 ⟨c.state, c.inputHead.val, c.workHead.val,
    27 fun i => if h : i < s then c.tape ⟨i, h⟩ else M.blank⟩
    28
    29end Lax307052.BoundedConfigurations
    30

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