We show that the Identity Problem is decidable in polynomial time for finitely generated sub-semigroups of the group $\mathsf{UT}(4, \mathbb{Z})$ of $4 \times 4$ unitriangular integer matrices. As a byproduct of our proof, we also show the polynomial-time decidability of several subset reachability problems in $\mathsf{UT}(4, \mathbb{Z})$.

翻译：我们显示,对于该组中有限生成的子小组 $\ mathsf{UT}( 4, \ mathbb}) $4\ times 4$ 单位形整数矩阵, 身份问题在多元时间内是可以判断的。 作为我们证据的副产品, 我们还用$\ mathsf{UT}( 4,\ mathbb} 4, \ mathbb} 来显示多个子子可达性问题的多数值- 时间递减性 。