License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2022.40
URN: urn:nbn:de:0030-drops-168380
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16838/
D'Costa, Julian ;
Karimov, Toghrul ;
Majumdar, Rupak ;
Ouaknine, Joël ;
Salamati, Mahmoud ;
Worrell, James
The Pseudo-Reachability Problem for Diagonalisable Linear Dynamical Systems
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.
BibTeX - Entry
@InProceedings{dcosta_et_al:LIPIcs.MFCS.2022.40,
author = {D'Costa, Julian and Karimov, Toghrul and Majumdar, Rupak and Ouaknine, Jo\"{e}l and Salamati, Mahmoud and Worrell, James},
title = {{The Pseudo-Reachability Problem for Diagonalisable Linear Dynamical Systems}},
booktitle = {47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
pages = {40:1--40:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-256-3},
ISSN = {1868-8969},
year = {2022},
volume = {241},
editor = {Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16838},
URN = {urn:nbn:de:0030-drops-168380},
doi = {10.4230/LIPIcs.MFCS.2022.40},
annote = {Keywords: pseudo-orbits, Orbit problem, Skolem problem, linear dynamical systems, reachability}
}
Keywords: |
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pseudo-orbits, Orbit problem, Skolem problem, linear dynamical systems, reachability |
Collection: |
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47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022) |
Issue Date: |
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2022 |
Date of publication: |
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22.08.2022 |