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Decidability and Complexity Borders of Reachability Problems (Invited Talk)

Author Georg Zetzsche

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Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
Keywords
  • infinite-state systems
  • pushdown
  • vector addition systems
  • reachability
  • decidability
  • complexity

Metrics

Abstract

Reachability problems are arguably one of the most fundamental type of decision problems in the area of infinite-state system: Essentially every non-trivial decision problem involves solving reachability problems of one kind or another.
Because of this, reachability has continuously received attention since the very early days of automata theory. It therefore seems worthwhile to characterize the decidability and complexity borders of reachability problems. By this we mean results that consider a family of decision problems and describe precisely where, within this family, a decidability or complexity border lies.
The talk will focus on two such settings: One is about decidability, where we aim to describe the state spaces for which reachability is decidable. The other is about complexity, where we aim to describe which kinds of target sets permit polynomial-time algorithms.

Cite As Get BibTex

Georg Zetzsche. Decidability and Complexity Borders of Reachability Problems (Invited Talk). In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 2:1-2:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.2

Author Details

Georg Zetzsche
  • Max Planck Institute for Software Systems (MPI-SWS), Kaiserslautern, Germany

Funding

Funded by the European Union (ERC, FINABIS, 101077902). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.

Acknowledgements

I am grateful to Roland Guttenberg for discussions that supported Conjecture 1.3.

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