We study a class of functional problems reducible to computing $f^{(n)}(x)$ for inputs $n$ and $x$, where $f$ is a polynomial-time bijection. As we prove, the definition is robust against variations in the type of reduction used in its definition, and in whether we require $f$ to have a polynomial-time inverse or to be computible by a reversible logic circuit. These problems are characterized by the complexity class $\mathsf{FP}^{\mathsf{PSPACE}}$, and include natural $\mathsf{FP}^{\mathsf{PSPACE}}$-complete problems in circuit complexity, cellular automata, graph algorithms, and the dynamical systems described by piecewise-linear transformations.

翻译：我们研究了一系列功能问题,可以用来计算投入的美元(n)}(x)美元和美元($),其中美元是多元时间的双弹。正如我们所证明的那样,定义针对其定义中使用的削减类型的变化,以及我们是否需要美元来进行多球时间反向计算或用可逆逻辑电路进行可比较。这些问题的特点是复杂等级($\mathsf{FP}mathsf{PSPACE},其中包括在电路复杂度、蜂窝自动数据、图表算法和以小线性变形描述的动态系统方面自然存在的问题。