Reachability in Two-Dimensional Vector Addition Systems with States: One Test Is for Free

Authors Jérôme Leroux, Grégoire Sutre

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Jérôme Leroux
  • LaBRI, Université Bordeaux, CNRS, Bordeaux-INP, Talence, France
Grégoire Sutre
  • LaBRI, Université Bordeaux, CNRS, Bordeaux-INP, Talence, France

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Jérôme Leroux and Grégoire Sutre. Reachability in Two-Dimensional Vector Addition Systems with States: One Test Is for Free. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 37:1-37:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Vector addition system with states is an ubiquitous model of computation with extensive applications in computer science. The reachability problem for vector addition systems is central since many other problems reduce to that question. The problem is decidable and it was recently proved that the dimension of the vector addition system is an important parameter of the complexity. In fixed dimensions larger than two, the complexity is not known (with huge complexity gaps). In dimension two, the reachability problem was shown to be PSPACE-complete by Blondin et al. in 2015. We consider an extension of this model, called 2-TVASS, where the first counter can be tested for zero. This model naturally extends the classical model of one counter automata (OCA). We show that reachability is still solvable in polynomial space for 2-TVASS. As in the work Blondin et al., our approach relies on the existence of small reachability certificates obtained by concatenating polynomially many cycles.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Counter machine
  • Vector addition system
  • Reachability problem
  • Formal verification
  • Infinite-state system


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