OAI/Combinatorics/Sensitivity/Model.lean

GitHub source file

5 declarations, 0 contain sorry, 0 declared as axioms

Literal Boolean flips and ordinary sensitivity measures. All maxima range over the actual finite input or block-family space.

  1. def OAI.Paper320.flip line 14

    Source documentation

    Flip exactly the coordinates belonging to the specified block.

    Also declared: ComparatorChallenges/SensitivitySeparation.lean:10 (same declaration text).

    def flip {I : Type} (x : I → Bool) (B : Finset I) : I → Bool :=
    …
  2. def OAI.Paper320.sensitivityAt line 18

    Source documentation

    The ordinary number of sensitive individual input coordinates.

    Also declared: ComparatorChallenges/SensitivitySeparation.lean:13 (same declaration text).

    def sensitivityAt {I : Type} [Fintype I]
        (f : (I → Bool) → Bool) (x : I → Bool) : ℕ :=
    …
  3. def OAI.Paper320.sensitivity line 23

    Source documentation

    Maximum ordinary sensitivity over all Boolean inputs.

    Also declared: ComparatorChallenges/SensitivitySeparation.lean:17 (same declaration text).

    def sensitivity {I : Type} [Fintype I] (f : (I → Bool) → Bool) : ℕ :=
    …
  4. def OAI.Paper320.blockSensitivityAt line 28

    Source documentation

    Maximum size of a family of disjoint nonempty sensitive blocks at an input. The empty family is allowed and contributes zero. Invalid families contribute zero.

    Also declared: ComparatorChallenges/SensitivitySeparation.lean:20 (same declaration text).

    def blockSensitivityAt {I : Type} [Fintype I]
        (f : (I → Bool) → Bool) (x : I → Bool) : ℕ :=
    …
  5. def OAI.Paper320.blockSensitivity line 36

    Source documentation

    Maximum block sensitivity over all Boolean inputs.

    Also declared: ComparatorChallenges/SensitivitySeparation.lean:27 (same declaration text).

    def blockSensitivity {I : Type} [Fintype I] (f : (I → Bool) → Bool) : ℕ :=
    …