15 Search Results for "Whiteland, Markus A."

Document
DOI: 10.4230/LIPIcs.STACS.2026.67
Pumping-Like Results for Copyless Cost Register Automata and Polynomially Ambiguous Weighted Automata

Authors: Filip Mazowiecki, Antoni Puch, and Daniel Smertnig

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
In this work we consider two rich subclasses of weighted automata over fields: polynomially ambiguous weighted automata and copyless cost register automata. Primarily we are interested in understanding their expressiveness power. Over the field of rationals and 1-letter alphabets, it is known that the two classes coincide; they are equivalent to linear recurrence sequences (LRS) whose exponential bases are roots of rationals. We develop a tool we call Pumping Sequence Families, which, by exploiting the simple single-letter behaviour of the models, yields two pumping-like results over arbitrary fields with unrestricted alphabets, one for each class. As a corollary of these results, we present examples proving that the two classes become incomparable over the field of rationals with unrestricted alphabets. We complement the results by analysing the zeroness and equivalence problems. For weighted automata (even unrestricted) these problems are well understood: there are polynomial time, and even NC² algorithms. For copyless cost register automata we show that the two problems are PSpace-complete, where the difficulty is to show the lower bound.
Cite as

Filip Mazowiecki, Antoni Puch, and Daniel Smertnig. Pumping-Like Results for Copyless Cost Register Automata and Polynomially Ambiguous Weighted Automata. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 67:1-67:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{mazowiecki_et_al:LIPIcs.STACS.2026.67,
  author =	{Mazowiecki, Filip and Puch, Antoni and Smertnig, Daniel},
  title =	{{Pumping-Like Results for Copyless Cost Register Automata and Polynomially Ambiguous Weighted Automata}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{67:1--67:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.67},
  URN =		{urn:nbn:de:0030-drops-255568},
  doi =		{10.4230/LIPIcs.STACS.2026.67},
  annote =	{Keywords: weighted automata, cost register automata, ambiguity, linear recurrence sequences, equivalence problem}
}
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
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.159
The Ultimate Signs of Second-Order Holonomic Sequences

Authors: Fugen Hagihara and Akitoshi Kawamura

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
A real-valued sequence f = {f(n)}_{n ∈ ℕ} is said to be second-order holonomic if it satisfies a linear recurrence f (n + 2) = P (n) f (n + 1) + Q (n) f (n) for all sufficiently large n, where P, Q ∈ ℝ(x) are rational functions. We study the ultimate sign of such a sequence, i.e., the repeated pattern that the signs of f (n) follow for sufficiently large n. For each P, Q we determine all ultimate signs that f can have, and show how they partition the space of initial values of f. This completes the prior work by Neumann, Ouaknine and Worrell, who have settled some restricted cases. As a corollary, it follows that when P, Q have rational coefficients, f either has an ultimate sign of length 1, 2, 3, 4, 6, 8 or 12, or never falls into a repeated sign pattern. We also give a partial algorithm that finds the ultimate sign of f (or tells that there is none) in almost all cases.
Cite as

Fugen Hagihara and Akitoshi Kawamura. The Ultimate Signs of Second-Order Holonomic Sequences. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 159:1-159:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hagihara_et_al:LIPIcs.ICALP.2025.159,
  author =	{Hagihara, Fugen and Kawamura, Akitoshi},
  title =	{{The Ultimate Signs of Second-Order Holonomic Sequences}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{159:1--159:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.159},
  URN =		{urn:nbn:de:0030-drops-235363},
  doi =		{10.4230/LIPIcs.ICALP.2025.159},
  annote =	{Keywords: Holonomic sequences, ultimate signs, Skolem Problem, Positivity Problem}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.163
Verification of Linear Dynamical Systems via O-Minimality of the Real Numbers

Authors: Toghrul Karimov

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
A discrete-time linear dynamical system (LDS) is given by an update matrix M ∈ ℝ^{d× d}, and has the trajectories ⟨s, Ms, M²s, …⟩ for s ∈ ℝ^d. Reachability-type decision problems of linear dynamical systems, most notably the Skolem Problem, lie at the forefront of decidability: typically, sound and complete algorithms are known only in low dimensions, and these rely on sophisticated tools from number theory and Diophantine approximation. Recently, however, o-minimality has emerged as a counterpoint to these number-theoretic tools that allows us to decide certain modifications of the classical problems of LDS without any dimension restrictions. In this paper, we first introduce the Decomposition Method, a framework that captures all applications of o-minimality to decision problems of LDS that are currently known to us. We then use the Decomposition Method to show decidability of the Robust Safety Problem (restricted to bounded initial sets) in arbitrary dimension: given a matrix M, a bounded semialgebraic set S of initial points, and a semialgebraic set T of unsafe points, it is decidable whether there exists ε > 0 such that all orbits that begin in the ε-ball around S avoid T.
Cite as

Toghrul Karimov. Verification of Linear Dynamical Systems via O-Minimality of the Real Numbers. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 163:1-163:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{karimov:LIPIcs.ICALP.2025.163,
  author =	{Karimov, Toghrul},
  title =	{{Verification of Linear Dynamical Systems via O-Minimality of the Real Numbers}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{163:1--163:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.163},
  URN =		{urn:nbn:de:0030-drops-235401},
  doi =		{10.4230/LIPIcs.ICALP.2025.163},
  annote =	{Keywords: Linear dynamical systems, reachability problems, o-minimality}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.20
Boundedness of Cost Register Automata over the Integer Min-Plus Semiring

Authors: Andrei Draghici, Radosław Piórkowski, and Andrew Ryzhikov

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
Cost register automata (CRAs) are deterministic automata with registers taking values from a fixed semiring. A CRA computes a function from words to values from this semiring. CRAs are tightly related to well-studied weighted automata. Given a CRA, the boundedness problem asks if there exists a natural number N such that for every word, the value of the CRA on this word does not exceed N. This problem is known to be undecidable for the class of linear CRAs over the integer min-plus semiring (ℤ∪{+∞}, min, +), but very little is known about its subclasses. In this paper, we study boundedness of copyless linear CRAs with resets over the integer min-plus semiring. We show that it is decidable for such CRAs with at most two registers. More specifically, we show that it is, respectively, NL-complete and in coNP if the numbers in the input are presented in unary and binary. We also provide complexity results for two classes with an arbitrary number of registers. Namely, we show that for CRAs that use the minimum operation only in the output function, boundedness is PSPACE-complete if transferring values to other registers is allowed, and is coNP-complete otherwise. Finally, for each f_i in the hierarchy of fast-growing functions, we provide a stateless CRA with i registers whose output exceeds N only on runs longer than f_i(N). Our construction yields a non-elementary lower bound already for four registers.
Cite as

Andrei Draghici, Radosław Piórkowski, and Andrew Ryzhikov. Boundedness of Cost Register Automata over the Integer Min-Plus Semiring. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 20:1-20:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{draghici_et_al:LIPIcs.CSL.2025.20,
  author =	{Draghici, Andrei and Pi\'{o}rkowski, Rados{\l}aw and Ryzhikov, Andrew},
  title =	{{Boundedness of Cost Register Automata over the Integer Min-Plus Semiring}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{20:1--20:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.20},
  URN =		{urn:nbn:de:0030-drops-227775},
  doi =		{10.4230/LIPIcs.CSL.2025.20},
  annote =	{Keywords: cost register automata, boundedness, decidability}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2024.32
Additive Word Complexity and Walnut

Authors: Pierre Popoli, Jeffrey Shallit, and Manon Stipulanti

Published in: LIPIcs, Volume 323, 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)

Abstract
In combinatorics on words, a classical topic of study is the number of specific patterns appearing in infinite sequences. For instance, many works have been dedicated to studying the so-called factor complexity of infinite sequences, which gives the number of different factors (contiguous subblocks of their symbols), as well as abelian complexity, which counts factors up to a permutation of letters. In this paper, we consider the relatively unexplored concept of additive complexity, which counts the number of factors up to additive equivalence. We say that two words are additively equivalent if they have the same length and the total weight of their letters is equal. Our contribution is to expand the general knowledge of additive complexity from a theoretical point of view and consider various famous examples. We show a particular case of an analog of the long-standing conjecture on the regularity of the abelian complexity of an automatic sequence. In particular, we use the formalism of logic, and the software Walnut, to decide related properties of automatic sequences. We compare the behaviors of additive and abelian complexities, and we also consider the notion of abelian and additive powers. Along the way, we present some open questions and conjectures for future work.
Cite as

Pierre Popoli, Jeffrey Shallit, and Manon Stipulanti. Additive Word Complexity and Walnut. In 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 323, pp. 32:1-32:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{popoli_et_al:LIPIcs.FSTTCS.2024.32,
  author =	{Popoli, Pierre and Shallit, Jeffrey and Stipulanti, Manon},
  title =	{{Additive Word Complexity and Walnut}},
  booktitle =	{44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)},
  pages =	{32:1--32:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-355-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{323},
  editor =	{Barman, Siddharth and Lasota, S{\l}awomir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2024.32},
  URN =		{urn:nbn:de:0030-drops-222218},
  doi =		{10.4230/LIPIcs.FSTTCS.2024.32},
  annote =	{Keywords: Combinatorics on words, Abelian complexity, Additive complexity, Automatic sequences, Walnut software}
}
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.MFCS.2022.79
On Extended Boundary Sequences of Morphic and Sturmian Words

Authors: Michel Rigo, Manon Stipulanti, and Markus A. Whiteland

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
Generalizing the notion of the boundary sequence introduced by Chen and Wen, the nth term of the 𝓁-boundary sequence of an infinite word is the finite set of pairs (u,v) of prefixes and suffixes of length 𝓁 appearing in factors uyv of length n+𝓁 (n ≥ 𝓁 ≥ 1). Otherwise stated, for increasing values of n, one looks for all pairs of factors of length 𝓁 separated by n-𝓁 symbols. For the large class of addable numeration systems U, we show that if an infinite word is U-automatic, then the same holds for its 𝓁-boundary sequence. In particular, they are both morphic (or generated by an HD0L system). We also provide examples of numeration systems and U-automatic words with a boundary sequence that is not U-automatic. In the second part of the paper, we study the 𝓁-boundary sequence of a Sturmian word. We show that it is obtained through a sliding block code from the characteristic Sturmian word of the same slope. We also show that it is the image under a morphism of some other characteristic Sturmian word.
Cite as

Michel Rigo, Manon Stipulanti, and Markus A. Whiteland. On Extended Boundary Sequences of Morphic and Sturmian Words. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 79:1-79:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{rigo_et_al:LIPIcs.MFCS.2022.79,
  author =	{Rigo, Michel and Stipulanti, Manon and Whiteland, Markus A.},
  title =	{{On Extended Boundary Sequences of Morphic and Sturmian Words}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{79:1--79:16},
  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/entities/document/10.4230/LIPIcs.MFCS.2022.79},
  URN =		{urn:nbn:de:0030-drops-168776},
  doi =		{10.4230/LIPIcs.MFCS.2022.79},
  annote =	{Keywords: Boundary sequences, Sturmian words, Numeration systems, Automata, Graph of addition}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2021.67
On Positivity and Minimality for Second-Order Holonomic Sequences

Authors: George Kenison, Oleksiy Klurman, Engel Lefaucheux, Florian Luca, Pieter Moree, Joël Ouaknine, Markus A. Whiteland, and James Worrell

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract
An infinite sequence ⟨u_n⟩_n of real numbers is holonomic (also known as P-recursive or P-finite) if it satisfies a linear recurrence relation with polynomial coefficients. Such a sequence is said to be positive if each u_n ≥ 0, and minimal if, given any other linearly independent sequence ⟨v_n⟩_n satisfying the same recurrence relation, the ratio u_n/v_n → 0 as n → ∞. In this paper we give a Turing reduction of the problem of deciding positivity of second-order holonomic sequences to that of deciding minimality of such sequences. More specifically, we give a procedure for determining positivity of second-order holonomic sequences that terminates in all but an exceptional number of cases, and we show that in these exceptional cases positivity can be determined using an oracle for deciding minimality.
Cite as

George Kenison, Oleksiy Klurman, Engel Lefaucheux, Florian Luca, Pieter Moree, Joël Ouaknine, Markus A. Whiteland, and James Worrell. On Positivity and Minimality for Second-Order Holonomic Sequences. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 67:1-67:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{kenison_et_al:LIPIcs.MFCS.2021.67,
  author =	{Kenison, George and Klurman, Oleksiy and Lefaucheux, Engel and Luca, Florian and Moree, Pieter and Ouaknine, Jo\"{e}l and Whiteland, Markus A. and Worrell, James},
  title =	{{On Positivity and Minimality for Second-Order Holonomic Sequences}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{67:1--67:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.67},
  URN =		{urn:nbn:de:0030-drops-145071},
  doi =		{10.4230/LIPIcs.MFCS.2021.67},
  annote =	{Keywords: Holonomic sequences, Minimal solutions, Positivity Problem}
}
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
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}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.79
All Growth Rates of Abelian Exponents Are Attained by Infinite Binary Words

Authors: Jarkko Peltomäki and Markus A. Whiteland

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
We consider repetitions in infinite words by making a novel inquiry to the maximum eventual growth rate of the exponents of abelian powers occurring in an infinite word. Given an increasing, unbounded function f: ℕ → ℝ, we construct an infinite binary word whose abelian exponents have limit superior growth rate f. As a consequence, we obtain that every nonnegative real number is the critical abelian exponent of some infinite binary word.
Cite as

Jarkko Peltomäki and Markus A. Whiteland. All Growth Rates of Abelian Exponents Are Attained by Infinite Binary Words. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 79:1-79:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{peltomaki_et_al:LIPIcs.MFCS.2020.79,
  author =	{Peltom\"{a}ki, Jarkko and Whiteland, Markus A.},
  title =	{{All Growth Rates of Abelian Exponents Are Attained by Infinite Binary Words}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{79:1--79:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.79},
  URN =		{urn:nbn:de:0030-drops-127481},
  doi =		{10.4230/LIPIcs.MFCS.2020.79},
  annote =	{Keywords: abelian equivalence, abelian power, abelian critical exponent}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2020.117
On Polynomial Recursive Sequences

Authors: Michaël Cadilhac, Filip Mazowiecki, Charles Paperman, Michał Pilipczuk, and Géraud Sénizergues

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
We study the expressive power of polynomial recursive sequences, a nonlinear extension of the well-known class of linear recursive sequences. These sequences arise naturally in the study of nonlinear extensions of weighted automata, where (non)expressiveness results translate to class separations. A typical example of a polynomial recursive sequence is b_n = n!. Our main result is that the sequence u_n = nⁿ is not polynomial recursive.
Cite as

Michaël Cadilhac, Filip Mazowiecki, Charles Paperman, Michał Pilipczuk, and Géraud Sénizergues. On Polynomial Recursive Sequences. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 117:1-117:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{cadilhac_et_al:LIPIcs.ICALP.2020.117,
  author =	{Cadilhac, Micha\"{e}l and Mazowiecki, Filip and Paperman, Charles and Pilipczuk, Micha{\l} and S\'{e}nizergues, G\'{e}raud},
  title =	{{On Polynomial Recursive Sequences}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{117:1--117:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.117},
  URN =		{urn:nbn:de:0030-drops-125240},
  doi =		{10.4230/LIPIcs.ICALP.2020.117},
  annote =	{Keywords: recursive sequences, expressive power, weighted automata, higher-order pushdown automata}
}
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