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prepare eval

Proved
ResourceScheduling.Graph.prepare_eval

by arexychen · Oct 2, 2026 · Mathlib 0df444a (Lean v4.33.1)

algorithmspolynomial-time

Unary parsing and the two length comparisons set the parameter, dimension, remaining word, and validity flag exactly as specified.

Preamble
import Definitions.Def_ResourceScheduling_Graph_ReductionProgram
open ResourceScheduling.Graph GraphReg GraphProgram
Formal statement
namespace ResourceScheduling.Graph
theorem prepare_eval (s : RAMState GraphReg) :
    (prepare.eval s).val t = (splitOnes s.word).1 ∧
    (prepare.eval s).val n = 3 * (splitOnes s.word).1 ∧
    (prepare.eval s).word = (splitOnes s.word).2.tail ∧
    (prepare.eval s).out = s.out ∧
    (prepare.eval s).val good =
      if (splitOnes s.word).2 ≠ [] ∧ (splitOnes s.word).2.tail.length =
        (3 * (splitOnes s.word).1) * (3 * (splitOnes s.word).1) then 1 else 0 := by sorry
end ResourceScheduling.Graph
Source
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.

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