有界歧义向量加法系统的语言包含问题是可判定的
Language Inclusion for Boundedly-Ambiguous Vector Addition Systems is Decidable
AI总结：
该论文研究了向量加法系统（VASS）的语言包含与等价问题，证明了有界歧义情形下包含可判定且为Ackermann完备，并指出技术可推广至良构转移系统。
摘要：
我们考虑带有状态（VASS）的向量加法系统，在由接受状态集合（更一般地，由某些向上封闭条件）定义的接受条件下的语言包含和语言等价问题。一般而言，即使对于一维VASS，语言等价问题也是不可判定的，因此为了获得可判定性，我们研究受限子类。一方面，我们证明了VASS在k-歧义VASS（对于任何自然数k）中的语言包含问题是可判定的，甚至属于Ackermann类。另一方面，我们证明了确定性VASS的语言等价问题已经是Ackermann难的。这两个结果意味着在若干可能的限制下，语言包含和等价问题具有Ackermann完备性。我们的一些技术还可以在更广泛的无限状态系统中应用，即对于良构转移系统的某个子类。
英文摘要：
We consider the problems of language inclusion and language equivalence for Vector Addition Systems with States (VASS) with the acceptance condition defined by the set of accepting states (and more generally by some upward-closed conditions). In general, the problem of language equivalence is undecidable even for one-dimensional VASS, thus to get decidability we investigate restricted subclasses. On the one hand, we show that the problem of language inclusion of a VASS in k-ambiguous VASS (for any natural k) is decidable and even in Ackermann. On the other hand, we prove that the language equivalence problem is already Ackermann-hard for deterministic VASS. These two results imply Ackermann-completeness for language inclusion and equivalence in several possible restrictions. Some of our techniques can be also applied in much broader generality in infinite-state systems, namely for some subclass of well-structured transition systems.
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