License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2021.30
URN: urn:nbn:de:0030-drops-144076
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Ajdarów, Michal ; Kučera, Antonín

Deciding Polynomial Termination Complexity for VASS Programs

LIPIcs-CONCUR-2021-30.pdf (0.9 MB)


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.

BibTeX - Entry

  author =	{Ajdar\'{o}w, Michal and Ku\v{c}era, Anton{\'\i}n},
  title =	{{Deciding Polynomial Termination Complexity for VASS Programs}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{30:1--30:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-203-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{203},
  editor =	{Haddad, Serge and Varacca, Daniele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-144076},
  doi =		{10.4230/LIPIcs.CONCUR.2021.30},
  annote =	{Keywords: Termination complexity, vector addition systems}

Keywords: Termination complexity, vector addition systems
Collection: 32nd International Conference on Concurrency Theory (CONCUR 2021)
Issue Date: 2021
Date of publication: 13.08.2021

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