{
  "abstract": "Given a finite set $A$ of natural numbers whose greatest common divisor is one, the Frobenius number $g(A)$ is the largest integer that is not a non-negative integer combination of the numbers in $A$. In a 2016 preprint, Matsubara states that given $A$ and $k$, deciding if $g(A) \\geq k$ is $Σ_2^P$-complete. A decade has passed since without peer-reviewed publication of this result. At the same time, the community has found it difficult to verify this result. In this note, we give a write-up of the completeness proof based on Matsubara (2016).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30036",
  "author_total": 1,
  "authors": [
    {
      "name": "Thomas Rothvoss"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f4ryz6d0nqfg6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30036",
  "fulltext_url": null,
  "id": "f4ryz6d0nqfg6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30036",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CC"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
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  "openalex": "W7204904732",
  "pdf_url": "https://arxiv.org/pdf/2608.30036",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f4ryz6d0nqfg6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30036",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30036"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A note on the $Σ_2^P$-completeness of the Frobenius number",
  "title_text": "A note on the Σ_2^P-completeness of the Frobenius number",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/f4ryz6d0nqfg6",
  "venue": "arXiv",
  "versions": []
}