Deciding Polynomial Termination Complexity for VASS Programs

Authors Michal Ajdarów , Antonín Kučera

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Michal Ajdarów
  • Masaryk University, Brno, Czech Republic
Antonín Kučera
  • Masaryk University, Brno, Czech Republic

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Michal Ajdarów and Antonín Kučera. Deciding Polynomial Termination Complexity for VASS Programs. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 30:1-30:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We show that for every fixed degree 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. 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
  • Termination complexity
  • vector addition systems


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