We prove that the genus of a regular language is decidable. For this purpose, we use a graph-theoretical approach. We show that the original question is equivalent to the existence of a special kind of graph epimorphism - a directed emulator morphism -- onto the underlying graph of the minimal deterministic automaton for the regular language. We also prove that the class of directed emulators of genus less than or equal to $g$ is closed under minors. Decidability follows from the Robertson-Seymour theorem.

中文翻译：

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常规语言和有向仿真器的属的可判定性

我们证明了正则语言的属是可判定的。为此，我们使用图论方法。我们证明了原始问题等价于在常规语言的最小确定性自动机的底层图上存在一种特殊的图同胚——有向仿真器态射。我们还证明了小于或等于 $g$ 属的有向模拟器类在未成年人下是封闭的。可判定性遵循 Robertson-Seymour 定理。