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Regular Separability in Büchi VASS

Authors Pascal Baumann , Roland Meyer , Georg Zetzsche

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Author Details

Pascal Baumann
  • Max Planck Institute for Software Systems (MPI-SWS), Kaiserslautern, Germany
Roland Meyer
  • TU Braunschweig, Germany
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. The second author was supported by the DFG project EDS@SYN: Effective Denotational Semantics for Synthesis.

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Pascal Baumann, Roland Meyer, and Georg Zetzsche. Regular Separability in Büchi VASS. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.STACS.2023.9

Abstract

We study the (ω-)regular separability problem for Büchi VASS languages: Given two Büchi VASS with languages L₁ and L₂, check whether there is a regular language that fully contains L₁ while remaining disjoint from L₂. We show that the problem is decidable in general and PSPACE-complete in the 1-dimensional case, assuming succinct counter updates. The results rely on several arguments. We characterize the set of all regular languages disjoint from L₂. Based on this, we derive a (sound and complete) notion of inseparability witnesses, non-regular subsets of L₁. Finally, we show how to symbolically represent inseparability witnesses and how to check their existence.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
Keywords
  • Separability problem
  • Vector addition systems
  • Infinite words
  • Decidability

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