{
  "abstract": "This study applies finite automata to the automatic solving of a variety of combinatorial games. For games whose positions and moves can be represented as regular languages and their operations, we design a two-stage automatic solving algorithm: first, construct a candidate finite automaton to determine the $\\mathcal{P}$- and $\\mathcal{N}$-positions, and then perform rigorous formal verification on this automaton; once verified, a complete solution of the game is obtained. For partizan octal games, we introduce a generalized misère quotient, overcoming the limitation that traditional theory applies only to impartial games. Using the above algorithm, we successfully solve the majority of two-digit partizan octal games, and based on these results, we propose a partizan version of Guy's conjecture. We also successfully solve a considerable number of partizan octal games under misère play, and give a conjecture on the structure of those games exhibiting ``algebraic periodicity'' among them. For Kotzig's nim, we resolve the most important related conjecture: we prove that the outcomes and SG values are periodic under both normal and misère play (including their partizan versions). Our algorithm successfully solves several small-scale cases, including misère play and partizan versions. This study pioneers a new theoretical tool and algorithmic paradigm for the automatic solving of combinatorial games, and has broad prospects for further extension and application in the field of combinatorial game theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.13273",
  "author_total": 1,
  "authors": [
    {
      "name": "Kai Liang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/40rwqzjhe4vkt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.13273",
  "fulltext_url": null,
  "id": "40rwqzjhe4vkt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.13273",
  "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": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|semigroups and automata theory"
    ]
  ],
  "openalex": "W7203442817",
  "pdf_url": "https://arxiv.org/pdf/2608.13273",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/40rwqzjhe4vkt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.13273",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.13273"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Finite Automaton Approach to Combinatorial Games",
  "title_text": "A Finite Automaton Approach to Combinatorial Games",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/40rwqzjhe4vkt",
  "venue": "arXiv",
  "versions": []
}