{
  "abstract": "Let $Λ=KQ/I$ be a finite-dimensional zero-relation algebra. We encode Crawley--Boevey tree modules over $Λ$ by finite rooted trees labelled by arrows of $Q$ and their formal inverses, and construct a deterministic finite bottom-up tree automaton recognizing exactly these encodings. We define an accepted tree to be an automata-induced tree brick when it has no non-trivial factor--image self-overlap, and use Crawley--Boevey's graph-map basis to prove that this is equivalent to brickness of the associated tree module. We also introduce local colourings of $Q_1$ and show that the arrow alphabet can be compressed without changing the tree data, graph maps, or brick property. The optimal number of colours for such a compression is the maximum of the in-degree and out-degree of $Q$. We conclude by asking whether the tree language consisting only of bricks is regular.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22406",
  "author_total": 1,
  "authors": [
    {
      "name": "Annoy Sengupta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1snv8b6ehvcc6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22406",
  "fulltext_url": null,
  "id": "1snv8b6ehvcc6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22406",
  "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.FL"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7214010769",
  "pdf_url": "https://arxiv.org/pdf/2609.22406",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1snv8b6ehvcc6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22406",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22406"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Tree Bricks and Finite Tree Automata",
  "title_text": "Tree Bricks and Finite Tree Automata",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/1snv8b6ehvcc6",
  "venue": "arXiv",
  "versions": []
}