{
  "abstract": "We revisit the complexity classification of constraint satisfaction problems (CSPs) for first-order reducts of $(\\mathbb{Z},<)$, established by Bodirsky, Martin, and Mottet in 2018. Following their approach, we give a self-contained proof of this classification, correcting several errors in the argument. We further show that, with the exception of cases arising from finite-domain CSPs, all tractable cases are solved by a well-known uniform algorithm, eliminating the need for the collection of ad-hoc algorithms used in the original paper. A central component of the proof allows the analysis to be restricted to first-order reducts of $(\\mathbb{Z},<)$ that contain the successor relation. We substantially simplify this reduction and generalize the underlying construction. This generalization allows us to apply the same technique to first-order reducts of the triangular lattice graph and of infinite regular trees, yielding a complete complexity classification for these classes of structures, in particular a $\\mathsf{P}$ versus $\\mathsf{NP}$-complete dichotomy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21967",
  "author_total": 1,
  "authors": [
    {
      "name": "Lukas Pieper"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8cwjagrqan71a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21967",
  "fulltext_url": null,
  "id": "8cwjagrqan71a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21967",
  "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.LO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7222607906",
  "pdf_url": "https://arxiv.org/pdf/2610.21967",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8cwjagrqan71a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21967",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21967"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Discrete Temporal CSPs et al",
  "title_text": "Discrete Temporal CSPs et al",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/8cwjagrqan71a",
  "venue": "arXiv",
  "versions": []
}