group-theory
Group-Theory-Collection
Group Theory Collection
A benchmark of 11.28 million permutation-composition problems over 94 finite groups, split by computational complexity class (TC⁰ vs NC¹).
Given a sequence of group elements, the task is to predict their composition. By Barrington's theorem, iterated composition in any fixed non-solvable group is NC¹-complete, while for solvable groups it lies in ACC⁰ ⊆ TC⁰. Architectures whose expressive power is bounded by TC⁰ — fixed-depth transformers and linear… See the full description on the dataset page: https://huggingface.co/datasets/BeeGass/Group-Theory-Collection.train_group_theory_cpt_1train_group_theory_cpttrain_group_theory_cpt_chunked_4096group_theory_distill