We introduce a linear extension of the rotor-routing model in directed graphs, akin to the sandpile model and vector addition systems, together with new rotor mechanisms that extend standard cyclic rotors. In this framework, rotor-routing is interpreted as the simultaneous movement of particles accross two coupled graphs, involving both vertex and arc-based particles. The standard, combinatorial rotor-routing of positive particles (legal routing) based on rotor-configurations, then becomes a special case of a linear equivalence. We give comprehensive reachability results characterizing legal routings among linear equivalences, expanding on previous results, and settle the algorithmic complexities associated with these problems.

翻译：本文提出了一种有向图中转子路由模型的线性扩展，该模型类似于沙堆模型与向量加法系统，并引入了扩展标准循环转子的新型转子机制。在此框架下，转子路由被解释为粒子在两个耦合图上的同步运动，涉及基于顶点和弧的粒子。基于转子构型的正粒子标准组合转子路由（合法路由）由此成为线性等价关系的一个特例。我们给出了刻画线性等价关系中合法路由的完整可达性结果，拓展了先前的研究结论，并确定了相关问题的算法复杂度。