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LLM2Cert: LLM Synthesis of Certificates with SMT/Lean Verification — arXiv:2610.30524

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.30524
License (as archived): CC0-1.0
Archived: 2026-10-23T15:14:58.777Z
SHA-256 of the archived text: d45eb0c3bf544579b99ec007b8b4d6442f1a5bfed8a8afd7752ccc91c8fc5e2d
Stable URL of this page: https://metraipolis.com/documento/dc_02da360b210e

How to cite

LLM2Cert: LLM Synthesis of Certificates with SMT/Lean Verification — arXiv:2610.30524 — arXiv (en), https://arxiv.org/abs/2610.30524 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_02da360b210e (Metraipolis archive dc_02da360b210e, sha256 d45eb0c3bf544579b99ec007b8b4d6442f1a5bfed8a8afd7752ccc91c8fc5e2d)

BibTeX

@misc{dc02da360b210e,
  title = {LLM2Cert: LLM Synthesis of Certificates with SMT/Lean Verification — arXiv:2610.30524},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.30524},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_02da360b210e; sha256 d45eb0c3bf544579b99ec007b8b4d6442f1a5bfed8a8afd7752ccc91c8fc5e2d},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.30524. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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 this https URL .

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.AI, nuovi lavori del giorno).
Categorie arXiv: Systems and Control (eess.SY) ; Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2610.30524 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-23T15:09:08.529Z dalla pagina https://arxiv.org/list/cs.AI/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).