{
  "abstract": "Lyapunov functions and barrier certificates give state-space guarantees of stability and safety, but synthesizing and verifying them---especially for nonlinear, high-dimensional systems---remains an open challenge. Existing pipelines verify candidates with numerical solvers (sum-of-squares programs), interval methods, or satisfiability-modulo-theories (SMT) solvers, which often require relaxations, are conservative, or scale poorly with model dimension and nonlinearity. These limitations have also shaped benchmark design: standard test suites are dominated by low-dimensional polynomial systems chosen to suit what solvers can handle rather than what engineering applications require. We address both sides of this challenge. First, we introduce DynaCertBench, a benchmark of 105 instances: 80 non-redundant systems curated from the literature, extended with high-dimensional and control-constrained variants and new nonlinearly coupled systems, comprehensively spanning stability, region-of-attraction, forward-invariance, and safety tasks. Second, we present LLM2Cert, an LLM-driven framework that synthesizes candidate certificates and verifies them against their proof obligations: each obligation is routed to an SMT solver or directly to the Lean Proof-Repair agent. On DynaCertBench, LLM2Cert verifies 81 of 105 instances ($77.1\\%$), a $17.1$ percentage point improvement over one-shot proposal without feedback. On the 81 fixed certificates, LLM2Cert verifies 22 that All-SMT leaves unresolved. Code and data are available at https://github.com/FormalCert-AI/llm2cert.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30524",
  "author_total": 9,
  "authors": [
    {
      "name": "Zhipeng Cao"
    },
    {
      "name": "Peiyang Song"
    },
    {
      "name": "Nikolaus Vertovec"
    },
    {
      "name": "Weiru Cui"
    },
    {
      "name": "Zhihao Yang"
    },
    {
      "name": "Mingkang Liu"
    },
    {
      "name": "Luxia Lin"
    },
    {
      "name": "Bai Xue"
    },
    {
      "name": "Alessandro Abate"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8dcbsga8tnskb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30524",
  "fulltext_url": null,
  "id": "8dcbsga8tnskb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30524",
  "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",
      "cs.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Formal Methods in Verification"
    ]
  ],
  "openalex": "W7223386416",
  "pdf_url": "https://arxiv.org/pdf/2610.30524",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8dcbsga8tnskb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30524",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30524"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "LLM2Cert: LLM Synthesis of Certificates with SMT/Lean Verification",
  "title_text": "LLM2Cert: LLM Synthesis of Certificates with SMT/Lean Verification",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/8dcbsga8tnskb",
  "venue": "arXiv",
  "versions": []
}