We study the problem of regular separability of languages of vector addition systems with states (VASS). It asks whether for two given VASS languages K and L, there exists a regular language R that includes K and is disjoint from L. While decidability of the problem in full generality remains an open question, there are several subclasses for which decidability has been shown: It is decidable for (i) one-dimensional VASS, (ii) VASS coverability languages, (iii) languages of integer VASS, and (iv) commutative VASS languages. We propose a general approach to deciding regular separability. We use it to decide regular separability of an arbitrary VASS language from any language in the classes (i), (ii), and (iii). This generalizes all previous results, including (iv).

中文翻译：

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矢量加法系统中正则可分性的一种方法

我们研究了具有状态的向量加法系统（VASS）的语言的规则可分性问题。它询问对于两个给定的 VASS 语言 K 和 L，是否存在包含 K 且与 L 不相交的常规语言 R。 ：对于 (i) 一维 VASS、(ii) VASS 可覆盖性语言、(iii) 整数 VASS 语言和 (iv) 可交换 VASS 语言，它是可判定的。我们提出了一种确定常规可分性的一般方法。我们使用它来确定任意 VASS 语言与类 (i)、(ii) 和 (iii) 中的任何语言的常规可分离性。这概括了所有先前的结果，包括（iv）。