AutomataBench/automata-bench

AutomataBench

AutomataBench evaluates whether a model can reconstruct the initial state of a reversible cellular automaton from revealed cells in its space-time evolution.

This Hugging Face dataset card is structured like a benchmark dataset repo. It uses Hub metadata front matter and an explicit configs block so the data can be loaded with datasets.load_dataset.

from datasets import load_dataset

ds = load_dataset("AutomataBench/automata-bench", split="sample")
print(ds[0].keys())

For local development before upload:

from datasets import load_dataset

ds = load_dataset("hf_dataset", split="sample")

Install the optional loader first if needed:

python3 -m pip install datasets

Fields

• id: stable row identifier.
• split: sample, public_dev, or public_eval.
• difficulty: easy, medium, or hard.
• task: currently initial_state_recovery.
• grid: width, height, and boundary.
• time_horizon: number of reversible automaton steps.
• rule: reversible 2x2 Margolus block rule, including binary alphabet, bit order, partition type, and 16-entry permutation.
• observations: revealed cells as (t, x, y, value) records.
• answer: reference answer with initial_state.
• metadata: full generator metadata.

Task

Return only JSON:

{"initial_state": [[0, 1], [1, 0]]}

with the actual instance dimensions. The answer is correct when simulating the provided reversible block cellular automaton from the returned initial state matches every observation.

Evaluation

Public splits include gold answers for local scoring. Do not include answer in model prompts. Scores on these public splits are useful for debugging, reproducibility, and public comparison, but they are not trusted official leaderboard scores because the answers are public. Official leaderboard scores use a separate non-public evaluation set.

The public verifier lives in the GitHub repo:

cd public_repo
automata-bench-verify path/to/public_split.jsonl

Dataset Creation

Each accepted sample was generated by:

1. sampling a reversible binary 2x2 Margolus block rule;
2. rejecting degenerate rules;
3. simulating a random initial state;
4. revealing cells from the simulated trace;
5. using a PySAT-backed SAT encoding to prove uniqueness by solving once, blocking the recovered initial state, and proving the blocked formula UNSAT;
6. rejecting instances solved by propagation alone or below the branch-count threshold.

All public instances have certified unique solutions. The SAT check finds the reference initial state, blocks that state, and proves the blocked formula UNSAT with Glucose4. Rows expose this as metadata.unique_solution = true.

This is a static public snapshot. The held-out private evaluation set used for the initial organizer-run leaderboard is not included here and was checked on 2026-06-24 to have zero rule_id overlap with sample, public_dev, and public_eval. The public_dev and public_eval splits were also checked to have zero exact-instance overlap and zero rule_id overlap.

Intended Use

This dataset is intended for evaluation and benchmark development.

License

The public AutomataBench dataset files and documentation are licensed under the Creative Commons Attribution 4.0 International License.

The AutomataBench name, logo, website, official leaderboard, and non-public evaluation or data assets are not licensed under this public dataset license.

For larger datasets, custom-generated evaluation suites, or commercial licensing, contact: data@automatabench.com.

Available Splits

• public_dev: 300 rows, 100 easy, 100 medium, 100 hard.
• public_eval: 300 rows, 75 easy, 100 medium, 125 hard.
• sample: 60 rows, 20 easy, 20 medium, 20 hard.

Observation density varies by difficulty in public v1: easy rows range from 0.35 to 0.45, medium rows from 0.234375 to 0.25, and hard rows from 0.1875 to 0.21875. Overall public v1 density ranges from 0.1875 to 0.45.

All public splits include answers. sample is a balanced quick-inspection excerpt from public data. Official leaderboard scoring uses a separate non-public evaluation set, not these public splits.