---
pretty_name: DynaCertBench
language:
- en
license: mit
size_categories:
- n<1K
tags:
- dynamical-systems
- formal-verification
- certificate-synthesis
- stability
- region-of-attraction
- safety
- benchmark
- arxiv:2610.30524
configs:
- config_name: default
  default: true
  data_files:
  - split: test
    path: data/test.jsonl
---

# 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](https://arxiv.org/abs/2610.30524).

- [Code and original dataset](https://github.com/FormalCert-AI/llm2cert)
- [Project website](https://formalcert-ai.github.io/llm2cert/)
- [Exact GitHub source snapshot](https://github.com/FormalCert-AI/llm2cert/tree/37b6a0484fc8b532bb29588b56f5993193c42fcc/data)

## 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

```python
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:

```python
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

```bibtex
@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}
}
```