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.
BooleanFunctions
.
code
.
DisagreementStability
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Imports
Init
Mathlib.Tactic.FieldSimp
Mathlib.Tactic.Linarith
Mathlib.Tactic.Positivity
Mathlib.Tactic.Ring
Atlas.BooleanFunctions.code.NoiseSensitivity
Imported by
BooleanFourier
.
disagreementProb
BooleanFourier
.
disagreementProb_eq
BooleanFourier
.
noiseSensitivityReal
BooleanFourier
.
noiseSensitivityReal_eq
BooleanFourier
.
noiseSensitivity_eq
source
noncomputable def
BooleanFourier
.
disagreementProb
{
n
:
ℕ
}
(
ρ
:
ℝ
)
(
f
:
(
Fin
n
→
Bool
)
→
ℝ
)
:
ℝ
Instances For
source
theorem
BooleanFourier
.
disagreementProb_eq
{
n
:
ℕ
}
(
ρ
:
ℝ
)
(
f
:
(
Fin
n
→
Bool
)
→
ℝ
)
:
disagreementProb
ρ
f
=
(
1
-
noiseStability
ρ
f
)
/
2
source
noncomputable def
BooleanFourier
.
noiseSensitivityReal
{
n
:
ℕ
}
(
δ
:
ℝ
)
(
f
:
(
Fin
n
→
Bool
)
→
ℝ
)
:
ℝ
Instances For
source
theorem
BooleanFourier
.
noiseSensitivityReal_eq
{
n
:
ℕ
}
(
δ
:
ℝ
)
(
f
:
(
Fin
n
→
Bool
)
→
ℝ
)
:
noiseSensitivityReal
δ
f
=
(
1
-
noiseStability
(
1
-
2
*
δ
)
f
)
/
2
source
theorem
BooleanFourier
.
noiseSensitivity_eq
{
n
:
ℕ
}
(
δ
:
ℝ
)
(
f
:
(
Fin
n
→
Bool
)
→
Bool
)
:
noiseSensitivity
δ
f
=
(
1
-
noiseStability
(
1
-
2
*
δ
)
fun (
x
:
Fin
n
→
Bool
) =>
boolToReal
(
f
x
)
)
/
2