{
  "abstract": "For a fixed integer r ≥ 2 , we prove that the compressed primitivity problem in the free group F r = F ( x 1 , … , x r ) is decidable in nondeterministic polynomial time. That is, for a straight-line program A over { x 1 , … , x r } ± 1 representing an element g ∈ F r , the problem of deciding whether g is primitive in F r belongs to NP , with input measured by the size of A . For r = 2 , we prove that this problem is decidable in deterministic polynomial time. We also show that, in every fixed rank r ≥ 2 , automorphic minimality of the conjugacy class of a compressed word in F r is decidable in deterministic polynomial time.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics and Statistics, Hunter College of CUNY, 695 Park Ave, New York, NY 10065, USA"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Ilya Kapovich"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7xr2ahxzftj8n.bib",
  "cited_by": 0,
  "doi": "10.1016/j.jaca.2026.100050",
  "fulltext_url": "http://www.sciencedirect.com/science/article/pii/S2772827726000082",
  "id": "7xr2ahxzftj8n",
  "issns": [
    "2772-8277"
  ],
  "landing_url": "https://doi.org/10.1016/j.jaca.2026.100050",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "lcc",
      "QA1-939"
    ],
    [
      "openalex",
      "1703|semigroups and automata theory"
    ]
  ],
  "openalex": "W7170789052",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": "Elsevier",
  "ris": "https://research.draconitic.com/paper/7xr2ahxzftj8n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:43:42Z",
      "native_id": "5fecb7cc6e034e159a0dca5d39c42519",
      "source": "doaj",
      "url": "https://doi.org/10.1016/j.jaca.2026.100050"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "lcc:QA1-939",
      "subfield": "general"
    }
  ],
  "title": "Compressed primitivity problem in free groups",
  "title_text": "Compressed primitivity problem in free groups",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T13:43:42Z",
  "url": "https://research.draconitic.com/paper/7xr2ahxzftj8n",
  "venue": "Journal of Computational Algebra",
  "versions": []
}