openAI-math-dataset / lean /OAI /Combinatorics /LowSpaceSubsetSum /Search /ComputedParentExecution.lean
| import OAI.Combinatorics.LowSpaceSubsetSum.Search.PreparedParentExecution | |
| import OAI.Combinatorics.LowSpaceSubsetSum.Search.ComputedParentFuels | |
| import OAI.Combinatorics.LowSpaceSubsetSum.Search.PreparedReaderBounds | |
| namespace OAI | |
| /-! # Executed parent setup, cached limits, and stopped collection -/ | |
| namespace LowSpaceSubsetSum.ComputedParentExecution | |
| variable {n : ℕ} | |
| def run (D : RepresentationParentData n) (F : IndexedMask n) (P : StoredRestriction n) | |
| (hF : F.semantic = D.signs) (B : ℕ) : PreparedParentExecution.Result D.input D.capacity × ℕ := | |
| let limits := ComputedParentFuels.run D | |
| let out := PreparedParentExecution.collect D F P hF B | |
| limits.1.first limits.1.second limits.1.control | |
| (out.1, limits.2 + out.2 + 2) | |
| theorem run_value (D : RepresentationParentData n) (F : IndexedMask n) (P : StoredRestriction n) | |
| (hF : F.semantic = D.signs) (B : ℕ) : | |
| (run D F P hF B).1 = PreparedParentExecution.project | |
| (StoredParentExecution.collect {D with maskRestriction := P.semantic} F hF B).1 := by | |
| apply PreparedParentExecution.collect_value | |
| · exact ComputedParentFuels.first_value D | |
| · exact ComputedParentFuels.second_value D | |
| · rw [ComputedParentFuels.control_value, ComputedParentFuels.first_value, | |
| ComputedParentFuels.second_value] | |
| theorem dictionary_value (D : RepresentationParentData n) (F : IndexedMask n) | |
| (P : StoredRestriction n) (hF : F.semantic = D.signs) (B : ℕ) : | |
| StoredDictionaryJoin.erase D.input D.capacity (run D F P hF B).1.dictionary = | |
| ({D with maskRestriction := P.semantic}.collect B).state.user := by | |
| rw [run_value] | |
| have hv := congrArg (fun out => out.state.user) | |
| (StoredParentExecution.collect_value {D with maskRestriction := P.semantic} F hF B) | |
| exact hv | |
| theorem run_work (D : RepresentationParentData n) (F : IndexedMask n) (P : StoredRestriction n) | |
| (hF : F.semantic = D.signs) (B C : ℕ) (hn : 10000 ≤ n) | |
| (hl : ∀ j, (D.pair j).left.occurrences.card ≤ C) | |
| (hr : ∀ j, (D.pair j).right.occurrences.card ≤ C) (hC : C ≤ 2 ^ n) | |
| (hcopy : (12 * n + 32) * | |
| 2 ^ (Nat.clog 2 ({D with maskRestriction := P.semantic}.pair 1).leftArray.size + 1) ≤ B) : | |
| (run D F P hF B).2 ≤ | |
| 2 * inputScale D.input ^ 9 * (C + 1) + inputScale D.input ^ 3 + 7 + | |
| inputScale D.input ^ 6 * (({D with maskRestriction := P.semantic}.collect B).state.queries + | |
| ({D with maskRestriction := P.semantic}.collect B).state.reports + 1) + | |
| B * ({D with maskRestriction := P.semantic}.collect B).state.copies := by | |
| have hdepth (j : Fin 2) : | |
| Nat.clog 2 ({D with maskRestriction := P.semantic}.pair j).leftArray.size ≤ n := by | |
| have hd := PreparedReaderContext.build_depth D F P hF j ((hl j).trans hC) | |
| rw [PreparedReaderContext.build_value] at hd | |
| exact hd | |
| have hp := PreparedParentExecution.collect_work D F P hF B | |
| (ComputedParentFuels.run D).1.first (ComputedParentFuels.run D).1.second | |
| (ComputedParentFuels.run D).1.control C | |
| (ComputedParentFuels.first_value D) (ComputedParentFuels.second_value D) | |
| (by rw [ComputedParentFuels.control_value, ComputedParentFuels.first_value, | |
| ComputedParentFuels.second_value]) hn hl hr hC (hdepth 0) (hdepth 1) hcopy | |
| have hf := ComputedParentFuels.run_scale D hn | |
| change (ComputedParentFuels.run D).2 + | |
| (PreparedParentExecution.collect D F P hF B (ComputedParentFuels.run D).1.first | |
| (ComputedParentFuels.run D).1.second (ComputedParentFuels.run D).1.control).2 + 2 ≤ _ | |
| omega | |
| end LowSpaceSubsetSum.ComputedParentExecution | |
| end OAI | |