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97c3405 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 | import OAI.Combinatorics.ContingencyTables.Machines.BinaryPowerProgram
namespace OAI
/-! # Reusing a unary allowance across a binary transition table -/
namespace ContingencyTables.BoundedPowerPrograms
open MatchingFPRAS MatchingFPRAS.TreeTyped
def powerInput (z : List Bool×ℕ) : ℕ×ℕ := (2,z.1.length-z.2)
def powerInputRealizer : Realizer powerInput :=
pair (constant 2) (composition (pair (composition first listLength) second) subtract)
lemma polynomial_powerInput : PolynomialTime powerInputRealizer :=
polynomial_pair (polynomial_constant 2) (polynomial_composition (polynomial_pair
(polynomial_composition polynomial_first polynomial_listLength) polynomial_second)
polynomial_subtract)
def power (z : List Bool×ℕ) : ℕ := BinaryPowerPrograms.power (powerInput z)
def powerRealizer : Realizer power :=
composition powerInputRealizer BinaryPowerPrograms.powerRealizer
/-- A single allowance list can be shared by all entries in the finite
matrix. Each binary power then has polynomial cost in the supplied data. -/
theorem polynomial_power : PolynomialTime powerRealizer := by
apply work_composition polynomial_powerInput BinaryPowerPrograms.work_power (Polynomial.X+9)
intro z
have hl: z.1.length ≤ weight z := (list_length_le_weight z.1).trans (weight_fst z)
have hw : weight (2:ℕ)≤9 := by decide
simp only [powerInput,Polynomial.eval_add,Polynomial.eval_X,Polynomial.eval_ofNat]
omega
theorem power_eq (xs : List Bool) (gap : ℕ) : power (xs,gap)=2^(xs.length-gap) :=
BinaryPowerPrograms.power_eq 2 (xs.length-gap)
end ContingencyTables.BoundedPowerPrograms
end OAI
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