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ae00908 | 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 | import OAI.Algebra.FormulaHitting.GeneratorCost
import OAI.Algebra.FormulaHitting.BitRefinement
namespace OAI
namespace NCHitting
def primitiveBitBound (n s : ℕ) : ℕ := 1024 * generatorCostBound n s ^ 3
def generatorBitTrace (n s : ℕ) : BitRefinement.Trace :=
BitRefinement.Step.input [n, s] :: BitRefinement.programTrace [n, s] generatorProgram
theorem generatorBitTrace_executes (n s : ℕ) :
BitRefinement.Exec generatorProgram [n, s] (generate n s).output
(BitRefinement.Trace.steps (generatorBitTrace n s)) :=
⟨BitRefinement.programTrace [n, s] generatorProgram,
BitRefinement.programTrace_correct [n, s] generatorProgram, rfl⟩
theorem generate_primitive_bit_bound (n s : ℕ) :
BitRefinement.Exec generatorProgram [n, s] (generate n s).output
(BitRefinement.executionSteps generatorProgram [n, s]) ∧
BitRefinement.executionSteps generatorProgram [n, s] ≤ primitiveBitBound n s := by
refine ⟨BitRefinement.executionSteps_exec generatorProgram [n, s],
(BitRefinement.executionSteps_le generatorProgram [n, s]).trans ?_⟩
exact Nat.mul_le_mul_left 1024 (Nat.pow_le_pow_left (generate_cost_le n s) 3)
end NCHitting
end OAI
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