3 Search Results for "Ratschan, Stefan"

Document
DOI: 10.4230/LIPIcs.MFCS.2025.79
Deciding Robust Instances of an Escape Problem for Dynamical Systems in Euclidean Space

Authors: Eike Neumann

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
We study the problem of deciding whether a point escapes a closed subset of ℝ^d under the iteration of a continuous map f : ℝ^d → ℝ^d in the bit-model of real computation. We give a sound partial decision method for this problem which is complete in the sense that its halting set contains the halting set of all sound partial decision methods for the problem. Equivalently, our decision method terminates on all problem instances whose answer is robust under all sufficiently small perturbations of the function. We further show that the halting set of our algorithm is dense in the set of all problem instances. While our algorithm applies to general continuous functions, we demonstrate that it also yields complete decision methods for much more rigid function families: affine linear systems and quadratic complex polynomials. In the latter case, completeness is subject to the density of hyperbolicity conjecture in complex dynamics. This in particular yields an alternative proof of Hertling’s (2004) conditional answer to a question raised by Penrose (1989) regarding the computability of the Mandelbrot set.
Cite as

Eike Neumann. Deciding Robust Instances of an Escape Problem for Dynamical Systems in Euclidean Space. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 79:1-79:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{neumann:LIPIcs.MFCS.2025.79,
  author =	{Neumann, Eike},
  title =	{{Deciding Robust Instances of an Escape Problem for Dynamical Systems in Euclidean Space}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{79:1--79:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.79},
  URN =		{urn:nbn:de:0030-drops-241866},
  doi =		{10.4230/LIPIcs.MFCS.2025.79},
  annote =	{Keywords: Dynamical Systems, Computability in Analysis, Non-Linear Functions}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.76
Deciding Predicate Logical Theories Of Real-Valued Functions

Authors: Stefan Ratschan

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
The notion of a real-valued function is central to mathematics, computer science, and many other scientific fields. Despite this importance, there are hardly any positive results on decision procedures for predicate logical theories that reason about real-valued functions. This paper defines a first-order predicate language for reasoning about multi-dimensional smooth real-valued functions and their derivatives, and demonstrates that - despite the obvious undecidability barriers - certain positive decidability results for such a language are indeed possible.
Cite as

Stefan Ratschan. Deciding Predicate Logical Theories Of Real-Valued Functions. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 76:1-76:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{ratschan:LIPIcs.MFCS.2023.76,
  author =	{Ratschan, Stefan},
  title =	{{Deciding Predicate Logical Theories Of Real-Valued Functions}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{76:1--76:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.76},
  URN =		{urn:nbn:de:0030-drops-186101},
  doi =		{10.4230/LIPIcs.MFCS.2023.76},
  annote =	{Keywords: decision procedures, first-order predicate logical theories, real numbers, real-valued functions}
}
Document
DOI: 10.4230/LITES-v004-i001-a004
How Is Your Satellite Doing? Battery Kinetics with Recharging and Uncertainty

Authors: Holger Hermanns, Jan Krčál, and Gilles Nies

Published in: LITES, Volume 4, Issue 1 (2017). Leibniz Transactions on Embedded Systems, Volume 4, Issue 1

Abstract
The kinetic battery model is a popular model of the dynamic behaviour of a conventional battery, useful to predict or optimize the time until battery depletion. The model however lacks certain obvious aspects of batteries in-the-wild, especially with respect to the effects of random influences and the behaviour when charging up to capacity limits.This paper considers the kinetic battery model with limited capacity in the context of piecewise constant yet random charging and discharging. We provide exact representations of the battery behaviour wherever possible, and otherwise develop safe approximations that bound the probability distribution of the battery state from above and below. The resulting model enables the time-dependent evaluation of the risk of battery depletion. This is demonstrated in an extensive dependability study of a nano satellite currently orbiting the earth.
Cite as

Holger Hermanns, Jan Krčál, and Gilles Nies. How Is Your Satellite Doing? Battery Kinetics with Recharging and Uncertainty. In LITES, Volume 4, Issue 1 (2017). Leibniz Transactions on Embedded Systems, Volume 4, Issue 1, pp. 04:1-04:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@Article{hermanns_et_al:LITES-v004-i001-a004,
  author =	{Hermanns, Holger and Kr\v{c}\'{a}l, Jan and Nies, Gilles},
  title =	{{How Is Your Satellite Doing? Battery Kinetics with Recharging and Uncertainty}},
  journal =	{Leibniz Transactions on Embedded Systems},
  pages =	{04:1--04:28},
  ISSN =	{2199-2002},
  year =	{2017},
  volume =	{4},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LITES-v004-i001-a004},
  URN =		{urn:nbn:de:0030-drops-192655},
  doi =		{10.4230/LITES-v004-i001-a004},
  annote =	{Keywords: Battery Power, Depletion Risk, Bounded Charging and Discharging, Stochastic Load, Distribution Bounds}
}
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