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On Continuous Pushdown VASS in One Dimension

Authors Guillermo A. Pérez , Shrisha Rao

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Author Details

Guillermo A. Pérez
  • University of Antwerp – Flanders Make, Antwerp, Belgium
Shrisha Rao
  • University of Antwerp – Flanders Make, Antwerp, Belgium

Funding

Work supported by the Flemish inter-university (iBOF) "DESCARTES" project.

Acknowledgements

We thank Georg Zetzsche for help with the hardness proofs in the model with lower bounds; A. R. Balasubramanian for his comments on an early version of this work, and Tim Leys and Ritam Raha for useful discussions on the topic of (continuous) counter automata.

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Guillermo A. Pérez and Shrisha Rao. On Continuous Pushdown VASS in One Dimension. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 34:1-34:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.CONCUR.2024.34

Abstract

A pushdown vector addition system with states (PVASS) extends the model of vector addition systems with a pushdown stack. The algorithmic analysis of PVASS has applications such as static analysis of recursive programs manipulating integer variables. Unfortunately, reachability analysis, even for one-dimensional PVASS is not known to be decidable. So, we relax the model of one-dimensional PVASS to make the counter updates continuous and show that in this case reachability, coverability, and boundedness are decidable in polynomial time. In addition, for the extension of the model with lower-bound guards on the states, we show that coverability and reachability are NP-complete, and boundedness is coNP-complete.

Subject Classification

ACM Subject Classification
  • Theory of computation → Grammars and context-free languages
  • Theory of computation → Concurrency
Keywords
  • Vector addition systems
  • Pushdown automata
  • Reachability

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References

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