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The Pseudo-Reachability Problem for Diagonalisable Linear Dynamical Systems

Authors Julian D'Costa , Toghrul Karimov , Rupak Majumdar , Joël Ouaknine , Mahmoud Salamati , James Worrell

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ACM Subject Classification
  • Theory of computation → Logic and verification
Keywords
  • pseudo-orbits
  • Orbit problem
  • Skolem problem
  • linear dynamical systems
  • reachability

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Abstract

We study fundamental reachability problems on pseudo-orbits of linear dynamical systems. Pseudo-orbits can be viewed as a model of computation with limited precision and pseudo-reachability can be thought of as a robust version of classical reachability. Using an approach based on o-minimality of ℝ_exp we prove decidability of the discrete-time pseudo-reachability problem with arbitrary semialgebraic targets for diagonalisable linear dynamical systems. We also show that our method can be used to reduce the continuous-time pseudo-reachability problem to the (classical) time-bounded reachability problem, which is known to be conditionally decidable.

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Julian D'Costa, Toghrul Karimov, Rupak Majumdar, Joël Ouaknine, Mahmoud Salamati, and James Worrell. The Pseudo-Reachability Problem for Diagonalisable Linear Dynamical Systems. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 40:1-40:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.MFCS.2022.40

Author Details

Julian D'Costa
  • Department of Computer Science, University of Oxford, UK
Toghrul Karimov
  • Max Planck Institute for Software Systems, Saarland Informatics Campus, Germany
Rupak Majumdar
  • Max Planck Institute for Software Systems, Kaiserslautern, Germany
Joël Ouaknine
  • Max Planck Institute for Software Systems, Saarland Informatics Campus, Germany
Mahmoud Salamati
  • Max Planck Institute for Software Systems, Kaiserslautern, Germany
James Worrell
  • Department of Computer Science, University of Oxford, UK

Funding

  • D'Costa, Julian: emmy.network foundation under the aegis of the Fondation de Luxembourg.
  • Majumdar, Rupak: DFG grant 389792660 as part of TRR 248 (see https://perspicuous-computing.science).
  • Ouaknine, Joël: DFG grant 389792660 as part of TRR 248 (see https://perspicuous-computing.science). Joël Ouaknine is also affiliated with Keble College, Oxford as http://emmy.network/ Fellow.

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