7 Search Results for "Jantsch, Simon"

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.2025.80
On Expansions of Monadic Second-Order Logic with Dynamical Predicates

Authors: Joris Nieuwveld and Joël Ouaknine

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

Abstract
Expansions of the monadic second-order (MSO) theory of the structure ⟨ℕ;<⟩ have been a fertile and active area of research ever since the publication of the seminal papers of Büchi and Elgot & Rabin on the subject in the 1960s. In the present paper, we establish decidability of the MSO theory of ⟨ℕ;<,P⟩, where P ranges over a large class of unary "dynamical" predicates, i.e., sets of non-negative values assumed by certain integer linear recurrence sequences. One of our key technical tools is the novel concept of (effective) prodisjunctivity, which we expect may also find independent applications further afield.
Cite as

Joris Nieuwveld and Joël Ouaknine. On Expansions of Monadic Second-Order Logic with Dynamical Predicates. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 80:1-80:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{nieuwveld_et_al:LIPIcs.MFCS.2025.80,
  author =	{Nieuwveld, Joris and Ouaknine, Jo\"{e}l},
  title =	{{On Expansions of Monadic Second-Order Logic with Dynamical Predicates}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{80:1--80:17},
  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.2025.80},
  URN =		{urn:nbn:de:0030-drops-241879},
  doi =		{10.4230/LIPIcs.MFCS.2025.80},
  annote =	{Keywords: Monadic second-order logic, linear recurrence sequences, decidability, Baker’s theorem}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.32
Resolving Nondeterminism by Chance

Authors: Soumyajit Paul, David Purser, Sven Schewe, Qiyi Tang, Patrick Totzke, and Di-De Yen

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract
History-deterministic automata are those in which nondeterministic choices can be correctly resolved stepwise: there is a strategy to select a continuation of a run given the next input letter so that if the overall input word admits some accepting run, then the constructed run is also accepting. Motivated by checking qualitative properties in probabilistic verification, we consider the setting where the resolver strategy can randomise and only needs to succeed with lower-bounded probability. We study the expressiveness of such stochastically-resolvable automata as well as consider the decision questions of whether a given automaton has this property. In particular, we show that it is undecidable to check if a given NFA is λ-stochastically resolvable. This problem is decidable for finitely-ambiguous automata. We also present complexity upper and lower bounds for several well-studied classes of automata for which this problem remains decidable.
Cite as

Soumyajit Paul, David Purser, Sven Schewe, Qiyi Tang, Patrick Totzke, and Di-De Yen. Resolving Nondeterminism by Chance. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 32:1-32:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{paul_et_al:LIPIcs.CONCUR.2025.32,
  author =	{Paul, Soumyajit and Purser, David and Schewe, Sven and Tang, Qiyi and Totzke, Patrick and Yen, Di-De},
  title =	{{Resolving Nondeterminism by Chance}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{32:1--32:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.32},
  URN =		{urn:nbn:de:0030-drops-239822},
  doi =		{10.4230/LIPIcs.CONCUR.2025.32},
  annote =	{Keywords: History-determinism, finite automata, probabilistic automata}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2022.10
Parameter Synthesis for Parametric Probabilistic Dynamical Systems and Prefix-Independent Specifications

Authors: Christel Baier, Florian Funke, Simon Jantsch, Toghrul Karimov, Engel Lefaucheux, Joël Ouaknine, David Purser, Markus A. Whiteland, and James Worrell

Published in: LIPIcs, Volume 243, 33rd International Conference on Concurrency Theory (CONCUR 2022)

Abstract
We consider the model-checking problem for parametric probabilistic dynamical systems, formalised as Markov chains with parametric transition functions, analysed under the distribution-transformer semantics (in which a Markov chain induces a sequence of distributions over states). We examine the problem of synthesising the set of parameter valuations of a parametric Markov chain such that the orbits of induced state distributions satisfy a prefix-independent ω-regular property. Our main result establishes that in all non-degenerate instances, the feasible set of parameters is (up to a null set) semialgebraic, and can moreover be computed (in polynomial time assuming that the ambient dimension, corresponding to the number of states of the Markov chain, is fixed).
Cite as

Christel Baier, Florian Funke, Simon Jantsch, Toghrul Karimov, Engel Lefaucheux, Joël Ouaknine, David Purser, Markus A. Whiteland, and James Worrell. Parameter Synthesis for Parametric Probabilistic Dynamical Systems and Prefix-Independent Specifications. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{baier_et_al:LIPIcs.CONCUR.2022.10,
  author =	{Baier, Christel and Funke, Florian and Jantsch, Simon and Karimov, Toghrul and Lefaucheux, Engel and Ouaknine, Jo\"{e}l and Purser, David and Whiteland, Markus A. and Worrell, James},
  title =	{{Parameter Synthesis for Parametric Probabilistic Dynamical Systems and Prefix-Independent Specifications}},
  booktitle =	{33rd International Conference on Concurrency Theory (CONCUR 2022)},
  pages =	{10:1--10:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-246-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{243},
  editor =	{Klin, Bartek and Lasota, S{\l}awomir and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2022.10},
  URN =		{urn:nbn:de:0030-drops-170732},
  doi =		{10.4230/LIPIcs.CONCUR.2022.10},
  annote =	{Keywords: Model checking, parametric Markov chains, distribution transformer semantics}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2021.28
The Orbit Problem for Parametric Linear Dynamical Systems

Authors: Christel Baier, Florian Funke, Simon Jantsch, Toghrul Karimov, Engel Lefaucheux, Florian Luca, Joël Ouaknine, David Purser, Markus A. Whiteland, and James Worrell

Published in: LIPIcs, Volume 203, 32nd International Conference on Concurrency Theory (CONCUR 2021)

Abstract
We study a parametric version of the Kannan-Lipton Orbit Problem for linear dynamical systems. We show decidability in the case of one parameter and Skolem-hardness with two or more parameters. More precisely, consider a d-dimensional square matrix M whose entries are algebraic functions in one or more real variables. Given initial and target vectors u,v ∈ ℚ^d, the parametric point-to-point orbit problem asks whether there exist values of the parameters giving rise to a concrete matrix N ∈ ℝ^{d× d}, and a positive integer n ∈ ℕ, such that N^{n} u = v. We show decidability for the case in which M depends only upon a single parameter, and we exhibit a reduction from the well-known Skolem Problem for linear recurrence sequences, suggesting intractability in the case of two or more parameters.
Cite as

Christel Baier, Florian Funke, Simon Jantsch, Toghrul Karimov, Engel Lefaucheux, Florian Luca, Joël Ouaknine, David Purser, Markus A. Whiteland, and James Worrell. The Orbit Problem for Parametric Linear Dynamical Systems. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 28:1-28:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{baier_et_al:LIPIcs.CONCUR.2021.28,
  author =	{Baier, Christel and Funke, Florian and Jantsch, Simon and Karimov, Toghrul and Lefaucheux, Engel and Luca, Florian and Ouaknine, Jo\"{e}l and Purser, David and Whiteland, Markus A. and Worrell, James},
  title =	{{The Orbit Problem for Parametric Linear Dynamical Systems}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{28:1--28:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-203-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{203},
  editor =	{Haddad, Serge and Varacca, Daniele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2021.28},
  URN =		{urn:nbn:de:0030-drops-144053},
  doi =		{10.4230/LIPIcs.CONCUR.2021.28},
  annote =	{Keywords: Orbit problem, parametric, linear dynamical systems}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ICALP.2021.1
From Verification to Causality-Based Explications (Invited Talk)

Authors: Christel Baier, Clemens Dubslaff, Florian Funke, Simon Jantsch, Rupak Majumdar, Jakob Piribauer, and Robin Ziemek

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
In view of the growing complexity of modern software architectures, formal models are increasingly used to understand why a system works the way it does, opposed to simply verifying that it behaves as intended. This paper surveys approaches to formally explicate the observable behavior of reactive systems. We describe how Halpern and Pearl’s notion of actual causation inspired verification-oriented studies of cause-effect relationships in the evolution of a system. A second focus lies on applications of the Shapley value to responsibility ascriptions, aimed to measure the influence of an event on an observable effect. Finally, formal approaches to probabilistic causation are collected and connected, and their relevance to the understanding of probabilistic systems is discussed.
Cite as

Christel Baier, Clemens Dubslaff, Florian Funke, Simon Jantsch, Rupak Majumdar, Jakob Piribauer, and Robin Ziemek. From Verification to Causality-Based Explications (Invited Talk). In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{baier_et_al:LIPIcs.ICALP.2021.1,
  author =	{Baier, Christel and Dubslaff, Clemens and Funke, Florian and Jantsch, Simon and Majumdar, Rupak and Piribauer, Jakob and Ziemek, Robin},
  title =	{{From Verification to Causality-Based Explications}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{1:1--1:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.1},
  URN =		{urn:nbn:de:0030-drops-140709},
  doi =		{10.4230/LIPIcs.ICALP.2021.1},
  annote =	{Keywords: Model Checking, Causality, Responsibility, Counterfactuals, Shapley value}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2020.36
Reachability in Dynamical Systems with Rounding

Authors: Christel Baier, Florian Funke, Simon Jantsch, Toghrul Karimov, Engel Lefaucheux, Joël Ouaknine, Amaury Pouly, David Purser, and Markus A. Whiteland

Published in: LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)

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.
Cite as

Christel Baier, Florian Funke, Simon Jantsch, Toghrul Karimov, Engel Lefaucheux, Joël Ouaknine, Amaury Pouly, David Purser, and Markus A. Whiteland. Reachability in Dynamical Systems with Rounding. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 36:1-36:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{baier_et_al:LIPIcs.FSTTCS.2020.36,
  author =	{Baier, Christel and Funke, Florian and Jantsch, Simon and Karimov, Toghrul and Lefaucheux, Engel and Ouaknine, Jo\"{e}l and Pouly, Amaury and Purser, David and Whiteland, Markus A.},
  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 =	{Saxena, Nitin and Simon, Sunil},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.36},
  URN =		{urn:nbn:de:0030-drops-132778},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.36},
  annote =	{Keywords: dynamical systems, rounding, reachability}
}
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