DynaCertBench

DynaCertBench contains 105 dynamical-system certification problems for evaluating certificate synthesis and verification. It accompanies LLM2Cert: LLM Synthesis of Certificates with SMT/Lean Verification.

• Code and original dataset
• Project website
• Exact GitHub source snapshot

Contents

Task	Value of task_type	Problems
Stability certification	stability	26
Region-of-attraction verification	roa	12
Forward-invariant set synthesis	invariant	13
Safety verification	safety	54
Total		105

The benchmark includes 80 literature-derived problems (literature), 11 extended problems (extended), and 14 new systems (ours). There are 90 continuous-time and 15 discrete-time problems; the recorded system dimensions range from 1 to 10.

This distribution contains benchmark questions. All original candidate fields are null. Model outputs, proof answers, and experiment execution records are outside this dataset distribution.

Load the dataset

import json
from datasets import load_dataset

dataset = load_dataset("FormalCert-AI/DynaCertBench")
problems = dataset["test"]
assert len(problems) == 105

row = problems[0]
problem = json.loads(row["problem_json"])
original_record = json.loads(row["executable_record_json"])
description = json.loads(row["descriptive_record_json"])

stability_problems = problems.filter(lambda row: row["task_type"] == "stability")

All 105 problems are exposed in a single test split for evaluation. This packaging does not introduce a training/validation partition or assert that these public problems are held out from model training.

Fields

Each row corresponds to one original executable record, in the original order.

Field	Meaning
record_id	Canonical problem identifier, e.g. DCB-LIT-P1-001
paper_system_number	System number in the paper
task_type	stability, roa, invariant, or safety
problem_name	Task description from the descriptive source
tier	literature, extended, or ours
dimension	Recorded state dimension
time_domain	continuous or discrete
dynamics	Original executable dynamics string
specification_latex	Original descriptive system specification
citations	Source citation keys, preserved from the descriptive record
problem_json	Complete original executable problem object, serialized as JSON
executable_record_json	Complete original executable record, serialized as JSON
descriptive_record_json	Complete original descriptive record, serialized as JSON

The JSON string fields preserve heterogeneous task schemas without dropping fields or converting numeric expressions. Use json.loads to recover the original objects. Display columns are copied from source fields; the serialized objects and original files remain the authoritative representations.

Original files and reproducibility

original/ contains byte-for-byte copies from GitHub commit 37b6a0484fc8b532bb29588b56f5993193c42fcc:

• dynacertbench_executable.json: complete inputs consumed by the LLM2Cert pipeline.
• dynacertbench_by_problem.json: grouped descriptions, source references, metadata, and problem definitions.
• benchmark_curation_counts.json: aggregate curation counts; this is not a second set of benchmark problems.
• README.md: original dataset directory documentation.

provenance.json records the repository, pinned commit, Git blob hashes, SHA-256 checksums, and conversion policy. The original JSON files can also be downloaded directly:

import json
from huggingface_hub import hf_hub_download

path = hf_hub_download(
    repo_id="FormalCert-AI/DynaCertBench",
    filename="original/dynacertbench_executable.json",
    repo_type="dataset",
)
with open(path, encoding="utf-8") as f:
    executable = json.load(f)

Intended use and limitations

Use the dataset to evaluate synthesis of Lyapunov functions, barrier certificates, and related policies and their verification. The dataset itself does not execute a verifier or establish a new proof. Consult the original problem assumptions, formal contracts, and the LLM2Cert repository when running experiments.

The descriptive data preserves source-status annotations such as documented, inferred, and specified, and provenance placeholders such as <LOCAL_PATH> already present in the public GitHub release. These placeholders are not downloadable source files. Consult the source references when reusing an individual literature-derived problem. The source material and the executable normalization can express different roles (for example, original versus normalized neighborhoods); both representations are retained unchanged.

License and attribution

The source repository is released under the MIT license, reproduced in LICENSE. CITATION.cff and THIRD_PARTY_NOTICES.md are retained from that same public commit. Preserve the individual problem source citations when reusing the benchmark.

Citation

@misc{cao2026llm2cert,
  title = {LLM2Cert: LLM Synthesis of Certificates with SMT/Lean Verification},
  author = {Cao, Zhipeng and Song, Peiyang and Vertovec, Nikolaus and
            Cui, Weiru and Yang, Zhihao and Liu, Mingkang and Lin, Luxia and
            Xue, Bai and Abate, Alessandro},
  year = {2026},
  eprint = {2610.30524},
  archivePrefix = {arXiv},
  primaryClass = {eess.SY},
  url = {https://arxiv.org/abs/2610.30524}
}