Improved Lower Bounds for Reachability in Vector Addition Systems

Authors Wojciech Czerwiński , Sławomir Lasota , Łukasz Orlikowski

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Author Details

Wojciech Czerwiński
  • University of Warsaw, Poland
Sławomir Lasota
  • University of Warsaw, Poland
Łukasz Orlikowski
  • University of Warsaw, Poland

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Wojciech Czerwiński, Sławomir Lasota, and Łukasz Orlikowski. Improved Lower Bounds for Reachability in Vector Addition Systems. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 128:1-128:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We investigate computational complexity of the reachability problem for vector addition systems (or, equivalently, Petri nets), the central algorithmic problem in verification of concurrent systems. Concerning its complexity, after 40 years of stagnation, a non-elementary lower bound has been shown recently: the problem needs a tower of exponentials of time or space, where the height of tower is linear in the input size. We improve on this lower bound, by increasing the height of tower from linear to exponential. As a side-effect, we obtain better lower bounds for vector addition systems of fixed dimension.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parallel computing models
  • Petri nets
  • vector addition systems
  • reachability problem


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