{
  "abstract": "We prove that deciding whether there is a surjective homomorphism from an arbitrary finitely presented inverse monoid onto the bicyclic monoid is $\\mathsf{NP}$-complete. As part of the proof, we show that an extension of existential Presburger arithmetic which involves greatest common divisors on $n$ arguments is in $\\mathsf{NP}$, extending a recent result of Défossez, Haase, Mansutti, and Pérez (SODA 2024).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08198",
  "author_total": 2,
  "authors": [
    {
      "name": "Luka Carroll"
    },
    {
      "name": "Murray Elder"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ab08m1387p47g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08198",
  "fulltext_url": null,
  "id": "ab08m1387p47g",
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  "landing_url": "https://arxiv.org/abs/2610.08198",
  "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": [
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      "arxiv",
      "cs.LO"
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      "arxiv",
      "math.GR"
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      "openalex",
      "1703|semigroups and automata theory"
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  "openalex": "W7220993078",
  "pdf_url": "https://arxiv.org/pdf/2610.08198",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ab08m1387p47g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.08198",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08198"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Testing epimorphism onto the bicyclic monoid is $\\mathsf{NP}$-complete",
  "title_text": "Testing epimorphism onto the bicyclic monoid is NP-complete",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/ab08m1387p47g",
  "venue": "arXiv",
  "versions": []
}