New Pumping Technique for 2-Dimensional VASS

Authors Wojciech Czerwiński , Sławomir Lasota , Christof Löding, Radosław Piórkowski

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Author Details

Wojciech Czerwiński
  • University of Warsaw, Poland
Sławomir Lasota
  • University of Warsaw, Poland
Christof Löding
  • RWTH Aachen, Germany
Radosław Piórkowski
  • University of Warsaw, Poland

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Wojciech Czerwiński, Sławomir Lasota, Christof Löding, and Radosław Piórkowski. New Pumping Technique for 2-Dimensional VASS. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 62:1-62:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


We propose a new pumping technique for 2-dimensional vector addition systems with states (2-VASS) building on natural geometric properties of runs. We illustrate its applicability by reproving an exponential bound on the length of the shortest accepting run, and by proving a new pumping lemma for languages of 2-VASS. The technique is expected to be useful for settling questions concerning languages of 2-VASS, e.g., for establishing decidability status of the regular separability problem.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
  • Theory of computation → Formal languages and automata theory
  • vector addition systems with states
  • pumping
  • decidability


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