| 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 |
|
|
