We consider the problems of language inclusion and language equivalence for Vector Addition Systems with States (VASSes) 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 VASSes, thus to get decidability we investigate restricted subclasses. On 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 Ackermann-hard already for deterministic VASSes. 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.

翻译：我们考虑具有状态集（更一般地，某些向上封闭条件）定义的接受条件的带状态向量加法系统（VASS）的语言包含与语言等价问题。通常，即使对一维VASS，语言等价问题也是不可判定的，因此为获得可判定性，我们研究受限子类。一方面，我们证明VASS对k-模糊VASS（对任意自然数k）的语言包含问题是可判定的，且其复杂度在Ackermann类中。另一方面，我们证明即使对确定性VASS，语言等价问题也是Ackermann难的。这两个结果意味着在若干可能的限制条件下，语言包含与等价问题具有Ackermann完全性。我们的部分技术还可更广泛地应用于无穷状态系统，即适用于良结构迁移系统的某个子类。