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How Fast Can You Escape a Compact Polytope?

Authors Julian D'Costa, Engel Lefaucheux, Joël Ouaknine, James Worrell

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  • Theory of computation → Timed and hybrid models
Keywords
  • Continuous linear dynamical systems
  • termination

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Abstract

The Continuous Polytope Escape Problem (CPEP) asks whether every trajectory of a linear differential equation initialised within a convex polytope eventually escapes the polytope. We provide a polynomial-time algorithm to decide CPEP for compact polytopes. We also establish a quantitative uniform upper bound on the time required for every trajectory to escape the given polytope. In addition, we establish iteration bounds for termination of discrete linear loops via reduction to the continuous case.

Cite As Get BibTex

Julian D'Costa, Engel Lefaucheux, Joël Ouaknine, and James Worrell. How Fast Can You Escape a Compact Polytope?. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 49:1-49:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.STACS.2020.49

Author Details

Julian D'Costa
  • Indian Institute of Science, Bangalore, India
  • Max Planck Institute for Software Systems, Saarland Informatics Campus, Germany
Engel Lefaucheux
  • Max Planck Institute for Software Systems, Saarland Informatics Campus, Germany
Joël Ouaknine
  • Max Planck Institute for Software Systems, Saarland Informatics Campus, Germany
  • Department of Computer Science, University of Oxford, UK
James Worrell
  • Department of Computer Science, University of Oxford, UK

Funding

  • Ouaknine, Joël: ERC grant AVS-ISS (648701) and DFG grant 389792660 as part of TRR 248 (see https://perspicuous-computing.science).
  • Worrell, James: EPSRC Fellowship EP/N008197/1.

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