{
  "schema_version": 1,
  "title": "Reproduction: Context-free Recognition with Transformers",
  "emoji": "\ud83c\udf32",
  "space_id": "ProCreations/repro-context-free-recognition-with-transformers",
  "paper": {
    "arxiv_id": "2601.01754"
  },
  "tags": [
    "icml2026-repro",
    "paper-JOyxs9ElI7"
  ],
  "updated_at": "2026-07-26T20:58:00+00:00",
  "root": {
    "slug": "index",
    "title": "Context-free recognition with transformers",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "file": "pages/executive-summary/page.md",
        "children": []
      },
      {
        "slug": "claim-0-judge-first-scorecard",
        "title": "Claim 0: Judge-first scorecard \u2014 six native verdicts",
        "file": "pages/claim-0-judge-first-scorecard/page.md",
        "children": []
      },
      {
        "slug": "claim-1-claim-1",
        "title": "Claim 1: Theorem 3.1 proves that all context-free languages can be recognized by looped transformers using O(log(n)) looping layers and O(n^6) padding tokens (Section 3, Theorem 3.1).",
        "file": "pages/claim-1-claim-1/page.md",
        "children": []
      },
      {
        "slug": "claim-2-claim-2",
        "title": "Claim 2: Theorem 4.1 shows unambiguous context-free languages can be recognized with fewer resources than the general case: O(log^2(n)) looping layers and O(n^3) padding tokens (Section 4, Theorem 4.1).",
        "file": "pages/claim-2-claim-2/page.md",
        "children": []
      },
      {
        "slug": "claim-3-claim-3",
        "title": "Claim 3: Theorem 4.2 further reduces requirements for unambiguous linear context-free languages to O(log(n)) looping layers and O(n^2) padding tokens by exploiting the linearity constraint (Section 4.2, Theorem 4.2).",
        "file": "pages/claim-3-claim-3/page.md",
        "children": []
      },
      {
        "slug": "claim-4-claim-4",
        "title": "Claim 4: Lemma 4.1 shows that Boolean formula evaluation can be computed in O(log(n)) steps via a parallel pebbling argument, which underlies the padding-token constructions used in the main theorems (Section 4, Lemma 4.1).",
        "file": "pages/claim-4-claim-4/page.md",
        "children": []
      },
      {
        "slug": "claim-5-claim-5",
        "title": "Claim 5: Corollary 4.1 shows that Boolean Formula Value Problem (BFVP) recognition requires zero padding tokens while retaining logarithmic depth (Section 4, Corollary 4.1).",
        "file": "pages/claim-5-claim-5/page.md",
        "children": []
      },
      {
        "slug": "claim-6-claim-6",
        "title": "Claim 6: Table 1 summarizes the padding-versus-depth tradeoff across general, unambiguous, and linear-unambiguous context-free language classes, showing that grammatical restrictions systematically reduce required padding (Table 1).",
        "file": "pages/claim-6-claim-6/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  },
  "agent_view_tokens": 9000,
  "revision": "1785061680000000000"
}