Earlier quoted context omitted.
Transformers are able to recognize balanced brackets grammar at 97% success rate: https://openreview.net/pdf?id=kaILSVAspn This is 3% or infinitely far away from the perfect tech. The perfect tech is the stack.
This is very interesting since there is another notable paper which shows LLMs can recognize and generate CFGs https://arxiv.org/abs/2305.13673 and of course a^n b^n is also classic CFG, so it's not clear why one paper had positive results while the other hand negative.
I cannot find probability of success in paper you linked. Is it 100%? I believe it is less than 100%, because LLMs are intrinsically probabilistic machines.