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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

Funding

This research was supported by Polish NCN grants "Separation problems in automata theory" (2016/21/D/ST6/01376), "Automatic analysis of concurrent systems" (2017/27/B/ST6/02093) and "Symbolic computations on first-order definable objects" (2016/21/B/ST6/01505).

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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)
https://doi.org/10.4230/LIPIcs.MFCS.2019.62

Abstract

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
Keywords
  • vector addition systems with states
  • pumping
  • decidability

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References

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