Deciding Polynomial Termination Complexity for VASS Programs
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We show that for every fixed k≥ 3, the problem whether the termination/counter complexity of a given demonic VASS is 𝒪(n^k), Ω(n^k), and Θ(n^k) is coNP-complete, NP-complete, and DP-complete, respectively. We also classify the complexity of these problems for k≤ 2. This shows that the polynomial-time algorithm designed for strongly connected demonic VASS in previous works cannot be extended to the general case. Then, we prove that the same problems for VASS games are PSPACE-complete. Again, we classify the complexity also for k≤ 2. Interestingly, tractable subclasses of demonic VASS and VASS games are obtained by bounding certain structural parameters, which opens the way to applications in program analysis despite the presented lower complexity bounds.
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