{
  "abstract": "Inspired by a statement about Extended Frege proof systems by Jain and Jin (FOCS 2022) we prove that: - there is a p-time binary relation $\\approx$ between circuits that implies their logical equivalence, - if the equivalence $C \\equiv D$ has an Extended Frege or a Circuit Frege proof with $k$ steps then there is a chain of circuits $E_i$ $$ C = E_0 \\approx \\dots \\approx E_t = D $$ with $t \\le O(k \\log k)$, and the total size of the chain is bounded above by $(k+|C|+|D|)^{O(1)}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.13367",
  "author_total": 1,
  "authors": [
    {
      "name": "Jan Krajicek"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/93hrk0cspd43p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.13367",
  "fulltext_url": null,
  "id": "93hrk0cspd43p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.13367",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CC"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7164587609",
  "pdf_url": "https://arxiv.org/pdf/2606.13367",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/93hrk0cspd43p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2606.13367",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.13367"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Extended Frege proofs, circuits and rewriting",
  "title_text": "Extended Frege proofs, circuits and rewriting",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/93hrk0cspd43p",
  "venue": "arXiv",
  "versions": []
}