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 $2V$.

翻译：Thompson集团的美元和Brin-Thompson集团的2V美元是有限的,可以定义为对比特字符串的单项行动,因此评价问题可以被界定为对比特字符串的对比特字符串的对比特字符串,因此,评价问题可以被界定为对V美元和2V美元。我们表明,这些评价问题减少为相应的字词问题,而总的来说,这些评价问题实际上等同于字词问题。评价问题的长期投入是没有确定性的环境和反向的确定性环境,对V美元、美元和P的2V美元没有确定性环境。