{
  "abstract": "In this article, we use the PBNF-transform, or Polynomial Boolean Normal Form, described earlier in two articles and now extended to higher arity, to solve Boolean satisfiability problems (SAT), which are part of the P versus NP problem. SAT consists of a statement of conjunctions of clauses, and in our SAT-solving models, we dualize the logical equations, inverting the problem by \\emph{multiplying} letters (literals) in the transferred clauses, now phrases: $pqrs\\cdots s_{\\ell}$, and using a binary iterated composition based on \\emph{adding polynomials} for the conjunctions in our solution formula. We obtain Polynomial Boolean Equations, PBE=0, by also renaming the truth value $1\\mapsto 0$(T). To find a solution, we look for repeating literals in the clauses to factor out. With reversed literal repetition, we can even reduce the CNF to the sum of the transformed clauses.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30523",
  "author_total": 1,
  "authors": [
    {
      "name": "Pelle Brooke Borgeke"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7g4pxc328g54h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30523",
  "fulltext_url": null,
  "id": "7g4pxc328g54h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30523",
  "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",
      "math.LO"
    ],
    [
      "openalex",
      "1703|Polynomial and algebraic computation"
    ]
  ],
  "openalex": "W7223330329",
  "pdf_url": "https://arxiv.org/pdf/2610.30523",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7g4pxc328g54h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30523",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30523"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "A Study in Solution Models for SAT using the PBNF-transform",
  "title_text": "A Study in Solution Models for SAT using the PBNF-transform",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/7g4pxc328g54h",
  "venue": "arXiv",
  "versions": []
}