向量加系统的正则可分性
An Approach to Regular Separability in Vector Addition Systems
摘要：
研究了状态向量加法系统语言的正则可分性问题。它询问对于两个给定的VASS语言K和L，是否存在一个包含K且与L不相交的正则语言R。虽然问题的可判定性仍然是一个开放的问题，但有几个子类已经证明了可判定性：它对（i）一维VASS，（ii）VASS覆盖性语言，（iii）整数VASS语言和（iv）交换VASS语言是可判定的。我们提出了一个一般的方法来确定定期可分性。我们用它来决定一个任意的VASS语言从类（i），（ii）和（iii）中的任何语言的正则可分性。这推广了所有以前的结果，包括（iv）。
英文摘要：
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).
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