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Deciding Polynomial Termination Complexity for VASS Programs by Ajdarów, Michal; Kučera, Antonín is a scholarly article available to read on EtoBox.

What is Deciding Polynomial Termination Complexity for VASS Programs about?

We show that for every fixed $k\geq 3$, the problem whether the termination/counter complexity of a given demonic VASS is $\mathcal{O}(n^k)$, $\Omega(n^{k})$, and $\Theta(n^{k})$ is coNP-complete, NP-complete, and DP-complete, respectively. We also classify the complexity of these problems for $k\leq 2$. 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 $k\leq 2$. 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.

Author

Ajdarów, Michal; Kučera, Antonín

Published

2021

Language

EN