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Coverability in 1-VASS with Disequality Tests

Authors Shaull Almagor , Nathann Cohen, Guillermo A. Pérez , Mahsa Shirmohammadi, James Worrell

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ACM Subject Classification
  • Theory of computation → Models of computation
Keywords
  • Reachability
  • Vector addition systems with states
  • Weighted graphs

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Abstract

We study a class of reachability problems in weighted graphs with constraints on the accumulated weight of paths. The problems we study can equivalently be formulated in the model of vector addition systems with states (VASS). We consider a version of the vertex-to-vertex reachability problem in which the accumulated weight of a path is required always to be non-negative. This is equivalent to the so-called control-state reachability problem (also called the coverability problem) for 1-dimensional VASS. We show that this problem lies in NC: the class of problems solvable in polylogarithmic parallel time. In our main result we generalise the problem to allow disequality constraints on edges (i.e., we allow edges to be disabled if the accumulated weight is equal to a specific value). We show that in this case the vertex-to-vertex reachability problem is solvable in polynomial time even though a shortest path may have exponential length. In the language of VASS this means that control-state reachability is in polynomial time for 1-dimensional VASS with disequality tests.

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Shaull Almagor, Nathann Cohen, Guillermo A. Pérez, Mahsa Shirmohammadi, and James Worrell. Coverability in 1-VASS with Disequality Tests. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 38:1-38:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.CONCUR.2020.38

Author Details

Shaull Almagor
  • Technion - Israel Institute of Technology, Haifa, Israel
Nathann Cohen
  • CNRS & LRI, Gif-sur-Yvette, France
Guillermo A. Pérez
  • University of Antwerp, Belgium
Mahsa Shirmohammadi
  • CNRS & IRIF, Université de Paris, France
James Worrell
  • University of Oxford, UK

Funding

  • Almagor, Shaull: has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 837327.
  • Worrell, James: Supported by EPSRC Fellowship EP/N008197/1.

Acknowledgements

We thank P. Offtermatt for pointing us to literature on NC-algorithms.

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