emit inner
ProvedResourceScheduling.Graph.emit_inneralgorithmspolynomial-time
The innermost resource-row emission loop appends exactly the canonical unary resource fields to the reversed output while preserving the numeric bound.
Preamble
import Definitions.Def_ResourceScheduling_Graph_ReductionProgram import Definitions.Def_ResourceScheduling_Graph_RAMSafe open ResourceScheduling.Graph GraphReg GraphProgram
Formal statement
namespace ResourceScheduling.Graph
theorem emit_inner (B N : ℕ) (s : RAMState GraphReg) (hs : RAMBound B s)
(hn : s.val n = N) (hpos : 1 ≤ B) :
RAMSafe (forN c2 k (by decide) emitCell) B s ∧
((forN c2 k (by decide) emitCell).eval s).out =
((List.range N).flatMap fun k => unary (if k = s.val i ∨ k = s.val j then 1 else 0)).reverse ++ s.out := by sorry
end ResourceScheduling.GraphSource
New auxiliary formalization for the ResourceScheduling Q2 reduction. The target is the unchanged CookPvsNP one-tape machine model, following Cook, The P versus NP problem, Clay Mathematics Institute (2000), Appendix. This explicit finite-column stack compiler and its simulation lemmas are new contributions, not numbered claims from Cook or the scheduling source paper.