openAI-math-dataset / lean /OAI /Combinatorics /LowSpaceSubsetSum /Word /WordSeedPrimeTestExecution.lean
| import OAI.Combinatorics.LowSpaceSubsetSum.Word.WordSeedPowerExecution | |
| import OAI.Combinatorics.LowSpaceSubsetSum.Storage.PrimeTestCells | |
| namespace OAI | |
| /-! # Prime testing with executed scalar initialization | |
| Both powers used by the test are produced by the doubling cursor. The | |
| divisor scan consumes the computed limit directly and retains scalar state. | |
| -/ | |
| namespace LowSpaceSubsetSum.WordSeedPrimeTestExecution | |
| def run (ell : ℕ) (p : Fin (2^ell)) : (Bool × ℕ) × ℕ := | |
| let modulus := WordSeedPowerExecution.run ell | |
| let limit := WordSeedPowerExecution.run ((ell+1)/2) | |
| let r := PrimeTestCells.scan p.val (limit.1-1) 2 0 | |
| ((decide (modulus.1 ≤ 4*ell*p.val) && (decide (2 ≤ p.val) && r.1.1.isNone), | |
| 12*r.1.2+modulus.2+limit.2+7), max 16 (r.2+16)) | |
| theorem run_value (ell : ℕ) (p : Fin (2^ell)) : | |
| (run ell p).1.1 = (SamplerAttempts.primeTest ell p).1 := by | |
| rw [← PrimeTestCells.test_value] | |
| simp only [run, WordSeedPowerExecution.run_value, PrimeTestCells.test, | |
| PrimeTestCells.divisors] | |
| theorem run_work (ell : ℕ) (p : Fin (2^ell)) : | |
| (run ell p).1.2 ≤ 12*2^((ell+1)/2)+12*(ell+1) := by | |
| have h := SamplerAttempts.divisorsBits_tests ell p | |
| rw [← PrimeTestCells.divisors_value] at h | |
| dsimp only [PrimeTestCells.divisors] at h | |
| simp only [run, WordSeedPowerExecution.run_value, WordSeedPowerExecution.run_work] | |
| omega | |
| theorem run_cells (ell : ℕ) (p : Fin (2^ell)) : (run ell p).2 = 28 := by | |
| simp only [run, PrimeTestCells.scan_cells] | |
| rfl | |
| end LowSpaceSubsetSum.WordSeedPrimeTestExecution | |
| end OAI | |