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DOI: 10.4230/LIPIcs.FSTTCS.2020.36
URN: urn:nbn:de:0030-drops-132778
URL: https://drops.dagstuhl.de/opus/volltexte/2020/13277/
Baier, Christel ; Funke, Florian ; Jantsch, Simon ; Karimov, Toghrul ; Lefaucheux, Engel ; Ouaknine, Joël ; Pouly, Amaury ; Purser, David ; Whiteland, Markus A.
Reachability in Dynamical Systems with Rounding
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Abstract
We consider reachability in dynamical systems with discrete linear updates, but with fixed digital precision, i.e., such that values of the system are rounded at each step. Given a matrix M ∈ ℚ^{d × d}, an initial vector x ∈ ℚ^{d}, a granularity g ∈ ℚ_+ and a rounding operation [⋅] projecting a vector of ℚ^{d} onto another vector whose every entry is a multiple of g, we are interested in the behaviour of the orbit 𝒪 = ⟨[x], [M[x]],[M[M[x]]],… ⟩, i.e., the trajectory of a linear dynamical system in which the state is rounded after each step. For arbitrary rounding functions with bounded effect, we show that the complexity of deciding point-to-point reachability - whether a given target y ∈ ℚ^{d} belongs to 𝒪 - is PSPACE-complete for hyperbolic systems (when no eigenvalue of M has modulus one). We also establish decidability without any restrictions on eigenvalues for several natural classes of rounding functions.
BibTeX - Entry
@InProceedings{baier_et_al:LIPIcs:2020:13277,
author = {Christel Baier and Florian Funke and Simon Jantsch and Toghrul Karimov and Engel Lefaucheux and Jo{\"e}l Ouaknine and Amaury Pouly and David Purser and Markus A. Whiteland},
title = {{Reachability in Dynamical Systems with Rounding}},
booktitle = {40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
pages = {36:1--36:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-174-0},
ISSN = {1868-8969},
year = {2020},
volume = {182},
editor = {Nitin Saxena and Sunil Simon},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/13277},
URN = {urn:nbn:de:0030-drops-132778},
doi = {10.4230/LIPIcs.FSTTCS.2020.36},
annote = {Keywords: dynamical systems, rounding, reachability}
}
| Keywords: | dynamical systems, rounding, reachability | |
| Seminar: | 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020) | |
| Issue date: | 2020 | |
| Date of publication: | 04.12.2020 |
