Integer Vector Addition Systems with States

  • Christoph Haase
  • Simon Halfon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8762)


This paper studies reachability, coverability and inclusion problems for Integer Vector Addition Systems with States (ℤ-VASS) and extensions and restrictions thereof. A ℤ-VASS comprises a finite-state controller with a finite number of counters ranging over the integers. Although it is folklore that reachability in ℤ-VASS is NP-complete, it turns out that despite their naturalness, from a complexity point of view this class has received little attention in the literature. We fill this gap by providing an in-depth analysis of the computational complexity of the aforementioned decision problems. Most interestingly, it turns out that while the addition of reset operations to ordinary VASS leads to undecidability and Ackermann-hardness of reachability and coverability, respectively, they can be added to ℤ-VASS while retaining NP-completeness of both coverability and reachability.


Inclusion Problem Register Machine Partial Word Presburger Arithmetic Linear Diophantine Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Christoph Haase
    • 1
  • Simon Halfon
    • 1
  1. 1.Laboratoire Spécification et Vérification (LSV)CNRS École Normale Supérieure (ENS) de CachanFrance

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