Evaluation problems for the Thompson group and the Brin-Thompson group, and their relation to the word problem
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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 deterministic context-free for V, and P-complete for 2V.
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