Datasets:
Formats:
json
Languages:
English
Size:
< 1K
ArXiv:
Tags:
dynamical-systems
formal-verification
certificate-synthesis
stability
region-of-attraction
safety
License:
| 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} | |
| } | |
| ``` | |