# Evaluation problems for the Thompson group and the Brin-Thompson group, and their relation to the word problem

@article{Birget2021EvaluationPF, title={Evaluation problems for the Thompson group and the Brin-Thompson group, and their relation to the word problem}, author={Jean-Camille Birget}, journal={ArXiv}, year={2021}, volume={abs/2111.08646} }

The Thompson group V , as well as the Brin-Thompson group 2V , is finitely generated and can be defined as a monoid acting on bitstrings, respectively pairs of bitstrings. Therefore evaluation problems can be defined for V and 2V . We show that these evaluation problems reduce to the corresponding word problems, and that in general, these evaluation problems are actually equivalent to the word problems. The long-input version of the evaluation problem is deterministic context-free and reverse…

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