Graph-walking automata (GWA) are finite-state devices that traverse graphs given as an input by following their edges; they have been studied both as a theoretical notion and as a model of pathfinding in robotics. If a graph is regarded as the set of memory configurations of a certain abstract machine, then various families of devices can be described as GWA: such are two-way finite automata, their multi-head and multi-tape variants, tree-walking automata and their extension with pebbles, picture-walking automata, space-bounded Turing machines, etc. This paper defines a transformation of an arbitrary deterministic GWA to a reversible GWA. This is done with a linear blow-up in the number of states, where the constant factor depends on the degree of the graphs being traversed. The construction directly applies to all basic models representable as GWA, and, in particular, subsumes numerous existing results for making individual models halt on every input.

图形遍历自动机（GWA）是一种有限状态设备，通过跟随其边缘遍历作为输入的图形。他们已经被作为一种理论概念和机器人技术中的寻路模型进行了研究。如果将图形视为某个抽象机器的内存配置集，则可以将各种设备系列描述为GWA：双向有限自动机，它们的多头和多带变体，树遍历自动机以及它们在鹅卵石，图像行走自动机，限界图灵机等方面的扩展。本文定义了将任意确定性GWA转换为可逆GWA的方法。这是通过状态数量的线性爆炸完成的，其中常数因子取决于所遍历图的程度。