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Leader election on a three-cycle

Lax755887.LeaderElection · concepts/Lax755887/LeaderElection.lean · lax-755887

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    Natural Language Statement

    Definition

    A protocol selects a unique position. Equivariance means that rotating the input rotates the output by the same amount. A uniform input cannot support both properties.

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    Lean source view on GitHub

    1import Mathlib
    2
    3/-!
    4---
    5title: Leader election on a three-cycle
    6type: definition
    7---
    8A protocol selects a unique position. Equivariance means that rotating the input rotates the output by the same amount. A uniform input cannot support both properties.
    9-/
    10
    11namespace Lax755887.LeaderElection
    12
    13abbrev State := Fin 3 → Bool
    14
    15def next (i : Fin 3) : Fin 3 := ⟨(i.val + 1) % 3, Nat.mod_lt _ (by decide)⟩
    16def rotate (s : State) : State := fun i => s (next i)
    17def UniqueLeader (run : State → State) : Prop := ∀ s, ∃! i, run s i = true
    18def Equivariant (run : State → State) : Prop := ∀ s, run (rotate s) = rotate (run s)
    19
    20structure Protocol where
    21 run : State → State
    22 elects : UniqueLeader run
    23
    24end Lax755887.LeaderElection
    25
    Builds on

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    From Mathlib

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