22 Search Results for "Gimbert, Hugo"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.98
Optimal Sequential Flows

Authors: Hugo Gimbert, Corto Mascle, and Patrick Totzke

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
We provide a new algebraic technique to solve the sequential flow problem in polynomial space. The task is to maximise the flow through a graph where edge capacities can be changed over time by choosing a sequence of capacity labelings from a given finite set. Our method is based on a novel factorization theorem for finite semigroups that, applied to a suitable flow semigroup, allows to derive small witnesses. This generalises to multiple in/output vertices, as well as regular constraints.
Cite as

Hugo Gimbert, Corto Mascle, and Patrick Totzke. Optimal Sequential Flows. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 98:1-98:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gimbert_et_al:LIPIcs.ICALP.2026.98,
  author =	{Gimbert, Hugo and Mascle, Corto and Totzke, Patrick},
  title =	{{Optimal Sequential Flows}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{98:1--98:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael 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.2026.98},
  URN =		{urn:nbn:de:0030-drops-264875},
  doi =		{10.4230/LIPIcs.ICALP.2026.98},
  annote =	{Keywords: Network Flow, Sequential Flow, Semigroup Factorization}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2026.180
Optimally Controlling a Random Population

Authors: Hugo Gimbert, Corto Mascle, and Patrick Totzke

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
The population control problem is a parameterised problem where a controller sends messages to a whole population of identical finite-state agents, aiming to eventually move them all into a target state. The decision problem asks whether this can be achieved for arbitrarily large finite populations. We focus on the randomised version of this problem, where every agent is a copy of the same finite Markov Decision Process and non-determinism in the global action chosen by the controller is resolved independently and uniformly at random. Colcombet, Fijalkow and Ohlmann [Thomas Colcombet et al., 2021] showed that this problem is decidable, but without any complexity upper bound. We show that the random population control problem is in fact ExpTime-complete.
Cite as

Hugo Gimbert, Corto Mascle, and Patrick Totzke. Optimally Controlling a Random Population. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 180:1-180:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gimbert_et_al:LIPIcs.ICALP.2026.180,
  author =	{Gimbert, Hugo and Mascle, Corto and Totzke, Patrick},
  title =	{{Optimally Controlling a Random Population}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{180:1--180:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael 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.2026.180},
  URN =		{urn:nbn:de:0030-drops-265685},
  doi =		{10.4230/LIPIcs.ICALP.2026.180},
  annote =	{Keywords: Controller synthesis, Parameterized verification}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.31
Lower Bounds for Ranking-Based Pivot Rules

Authors: Yann Disser, Georg Loho, Matthew Maat, and Nils Mosis

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

Abstract
The existence of a polynomial pivot rule for the simplex method for linear programming, policy iteration for Markov decision processes, and strategy improvement for parity games each are prominent open problems in their respective fields. While numerous natural candidates for efficient rules have been eliminated, all existing lower bound constructions are tailored to individual or small sets of pivot rules. We introduce a unified framework for formalizing classes of rules according to the information about the input that they rely on. Within this framework, we show lower bounds for ranking-based classes of rules that base their decisions on orderings of the improving pivot steps induced by the underlying data. Our first result is a superpolynomial lower bound for strategy improvement, obtained via a family of sink parity games, which applies to memory-based generalizations of Bland’s rule that only access the input by comparing the ranks of improving edges in some global order. Our second result is a subexponential lower bound for policy iteration, obtained via a family of Markov decision processes, which applies to memoryless rules that only access the input by comparing improving actions according to their ranks in a global order, their reduced costs, and the associated improvements in objective value. Both results carry over to the simplex method for linear programming.
Cite as

Yann Disser, Georg Loho, Matthew Maat, and Nils Mosis. Lower Bounds for Ranking-Based Pivot Rules. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{disser_et_al:LIPIcs.STACS.2026.31,
  author =	{Disser, Yann and Loho, Georg and Maat, Matthew and Mosis, Nils},
  title =	{{Lower Bounds for Ranking-Based Pivot Rules}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{31:1--31:19},
  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.2026.31},
  URN =		{urn:nbn:de:0030-drops-255207},
  doi =		{10.4230/LIPIcs.STACS.2026.31},
  annote =	{Keywords: lower bounds, Markov decision processes, parity games, pivot rules, policy iteration, simplex method}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.5
Distributed Games with a Central Decision Maker

Authors: Bharat Adsul and Nehul Jain

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
We study distributed games played on non-deterministic asynchronous automata which feature a central decision maker process that participates in all key decision making tasks. In these partial-information games, processes use their causal past to respond to scheduling choices made by the scheduler and cooperatively strategize as a team to achieve the winning objective. We show that the problem of deciding the existence of a distributed winning strategy is efficiently solvable for global safety and local parity objectives. We provide algorithmic solutions that match their computational hardness. We formulate the notion of a finite-state distributed strategy which allows to quantify its distributed memory requirements. For the aforementioned objectives, we establish that finite-state distributed winning strategies always exist. In fact, we provide novel constructions of such winning strategies which are shown to have almost optimal amount of distributed memory. We also show that a natural extension of the model with two decision making processes is undecidable.
Cite as

Bharat Adsul and Nehul Jain. Distributed Games with a Central Decision Maker. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 5:1-5:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{adsul_et_al:LIPIcs.FSTTCS.2025.5,
  author =	{Adsul, Bharat and Jain, Nehul},
  title =	{{Distributed Games with a Central Decision Maker}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{5:1--5:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.5},
  URN =		{urn:nbn:de:0030-drops-250843},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.5},
  annote =	{Keywords: Mazurkiewicz traces, models of concurrency, distributed synthesis, game-theoretic models, asynchronous automata, distributed decision-making}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.16
The Agafonov and Schnorr-Stimm Theorems for Probabilistic Automata

Authors: Laurent Bienvenu, Hugo Gimbert, and Subin Pulari

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
For a fixed alphabet A, an infinite sequence X is said to be normal if every word w over A appears in X with the same frequency as any other word of the same length. A classical result of Agafonov (1966) relates normality to finite automata as follows: a sequence X is normal if and only if any subsequence of X selected by a finite automaton is itself normal. Another theorem of Schnorr and Stimm (1972) gives an alternative characterization: a sequence X is normal if and only if no gambler can win large amounts of money by betting on the sequence X using a strategy that can be described by a finite automaton. Both of these theorems are established in the setting of deterministic finite automata. This raises the question as to whether they can be extended to the setting of probabilistic finite automata. In the case of the Agafonov theorem, a partial positive answer was given by Léchine et al. (MFCS 2024) in a restricted case of probabilistic automata with rational transition probabilities. In this paper, we settle the full conjecture by proving that both the Agafonov and the Schnorr-Stimm theorems hold true for arbitrary probabilistic automata. Specifically, we show that a sequence X is normal if and only if any probabilistic automaton selects a normal subsequence of X with probability 1 and also show that a sequence X is normal if and only if any probabilistic finite-state gambler fails to win on X with probability 1.
Cite as

Laurent Bienvenu, Hugo Gimbert, and Subin Pulari. The Agafonov and Schnorr-Stimm Theorems for Probabilistic Automata. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 16:1-16:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bienvenu_et_al:LIPIcs.FSTTCS.2025.16,
  author =	{Bienvenu, Laurent and Gimbert, Hugo and Pulari, Subin},
  title =	{{The Agafonov and Schnorr-Stimm Theorems for Probabilistic Automata}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{16:1--16:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.16},
  URN =		{urn:nbn:de:0030-drops-250978},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.16},
  annote =	{Keywords: Normality, Agafonov theorem, probabilistic automata}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.MFCS.2025.5
On Synthesis of Distributed Monitors (Invited Talk)

Authors: Anca Muscholl

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

Abstract
This talk addresses the synthesis problem of distributed monitors for concurrency properties.
Cite as

Anca Muscholl. On Synthesis of Distributed Monitors (Invited Talk). In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 5:1-5:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{muscholl:LIPIcs.MFCS.2025.5,
  author =	{Muscholl, Anca},
  title =	{{On Synthesis of Distributed Monitors}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{5:1--5:3},
  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.2025.5},
  URN =		{urn:nbn:de:0030-drops-241126},
  doi =		{10.4230/LIPIcs.MFCS.2025.5},
  annote =	{Keywords: Distributed synthesis, monitoring}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.31
Games with ω-Automatic Preference Relations

Authors: Véronique Bruyère, Christophe Grandmont, and Jean-François Raskin

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

Abstract
This paper investigates Nash equilibria (NEs) in multi-player turn-based games on graphs, where player preferences are modeled as ω-automatic relations via deterministic parity automata. Unlike much of the existing literature, which focuses on specific reward functions, our results apply to any preference relation definable by an ω-automatic relation. We analyze the computational complexity of determining the existence of an NE (possibly under some constraints), verifying whether a given strategy profile forms an NE, and checking whether a specific outcome can be realized by an NE. When a (constrained) NE exists, we show that there always exists one with finite-memory strategies. Finally, we explore fundamental properties of ω-automatic relations and their implications in the existence of equilibria.
Cite as

Véronique Bruyère, Christophe Grandmont, and Jean-François Raskin. Games with ω-Automatic Preference Relations. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bruyere_et_al:LIPIcs.MFCS.2025.31,
  author =	{Bruy\`{e}re, V\'{e}ronique and Grandmont, Christophe and Raskin, Jean-Fran\c{c}ois},
  title =	{{Games with \omega-Automatic Preference Relations}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{31:1--31:19},
  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.2025.31},
  URN =		{urn:nbn:de:0030-drops-241381},
  doi =		{10.4230/LIPIcs.MFCS.2025.31},
  annote =	{Keywords: Games played on graphs, Nash equilibrium, \omega-automatic relations, \omega-recognizable relations, constrained Nash equilibria existence problem}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.57
Resolving Nondeterminism with Randomness

Authors: Thomas A. Henzinger, Keya Prakash, and K. S. Thejaswini

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

Abstract
We define and study classes of ω-regular automata for which the nondeterminism can be resolved by a policy that uses a combination of memory and randomness on any input word, based solely on the prefix read so far. We examine two settings for providing the input word to an automaton. In the first setting, called adversarial resolvability, the input word is constructed letter-by-letter by an adversary, dependent on the resolver’s previous decisions. In the second setting, called stochastic resolvability, the adversary pre-commits to an infinite word and reveals it letter-by-letter. In each setting, we require the existence of an almost-sure resolver, i.e., a policy that ensures that as long as the adversary provides a word in the language of the underlying nondeterministic automaton, the run constructed by the policy is accepting with probability 1. The class of automata that are adversarially resolvable is the well-studied class of history-deterministic automata. The case of stochastically resolvable automata, on the other hand, defines a novel class. Restricting the class of resolvers in both settings to stochastic policies without memory introduces two additional new classes of automata. We show that the new automata classes offer interesting trade-offs between succinctness, expressivity, and computational complexity, providing a fine gradation between deterministic automata and nondeterministic automata.
Cite as

Thomas A. Henzinger, Keya Prakash, and K. S. Thejaswini. Resolving Nondeterminism with Randomness. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 57:1-57:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{henzinger_et_al:LIPIcs.MFCS.2025.57,
  author =	{Henzinger, Thomas A. and Prakash, Keya and Thejaswini, K. S.},
  title =	{{Resolving Nondeterminism with Randomness}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{57:1--57:18},
  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.2025.57},
  URN =		{urn:nbn:de:0030-drops-241645},
  doi =		{10.4230/LIPIcs.MFCS.2025.57},
  annote =	{Keywords: \omega-regular languages, History determinism, Stochastic strategies}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.66
Deciding Regular Games: a Playground for Exponential Time Algorithms

Authors: Zihui Liang, Bakh Khoussainov, and Mingyu Xiao

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

Abstract
Regular games form a well-established class of games for analysis and synthesis of reactive systems. They include colored Muller games, McNaughton games, Muller games, Rabin games, and Streett games. These games are played on directed graphs G where Player 0 and Player 1 play by generating an infinite path ρ through the graph. The winner is determined by specifications put on the set X of vertices in ρ that occur infinitely often. These games are determined, enabling the partitioning of G into two sets Win₀ and Win₁ of winning positions for Player 0 and Player 1, respectively. Numerous algorithms exist that decide instances of regular games, e.g., Muller games, by computing Win₀ and Win₁. In this paper we aim to find general principles for designing uniform algorithms that decide all regular games. For this we utilize various recursive and dynamic programming algorithms that leverage standard notions such as subgames and traps. Importantly, we show that our techniques improve or match the performances of existing algorithms for many instances of regular games.
Cite as

Zihui Liang, Bakh Khoussainov, and Mingyu Xiao. Deciding Regular Games: a Playground for Exponential Time Algorithms. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 66:1-66:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{liang_et_al:LIPIcs.MFCS.2025.66,
  author =	{Liang, Zihui and Khoussainov, Bakh and Xiao, Mingyu},
  title =	{{Deciding Regular Games: a Playground for Exponential Time Algorithms}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{66:1--66:18},
  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.2025.66},
  URN =		{urn:nbn:de:0030-drops-241732},
  doi =		{10.4230/LIPIcs.MFCS.2025.66},
  annote =	{Keywords: Regular games, colored Muller games, Rabin games, McNaughton games, Muller games, deciding games}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.86
Probabilistic Finite Automaton Emptiness Is Undecidable for a Fixed Automaton

Authors: Günter Rote

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

Abstract
We construct a probabilistic finite automaton (PFA) with 7 states and an input alphabet of 5 symbols for which the PFA Emptiness Problem is undecidable. The only input for the decision problem is the starting distribution. For the proof, we use reductions from special instances of the Post Correspondence Problem. We also consider some variations: The input alphabet of the PFA can be restricted to a binary alphabet at the expense of a larger number of states. If we allow a rational output value for each state instead of a yes-no acceptance decision, the number of states can even be reduced to 6.
Cite as

Günter Rote. Probabilistic Finite Automaton Emptiness Is Undecidable for a Fixed Automaton. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 86:1-86:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{rote:LIPIcs.MFCS.2025.86,
  author =	{Rote, G\"{u}nter},
  title =	{{Probabilistic Finite Automaton Emptiness Is Undecidable for a Fixed Automaton}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{86:1--86:18},
  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.2025.86},
  URN =		{urn:nbn:de:0030-drops-241930},
  doi =		{10.4230/LIPIcs.MFCS.2025.86},
  annote =	{Keywords: Probabilistic finite automaton, Undecidability, Post Correspondence Problem}
}
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.2025.7
Temporal Explorability Games

Authors: Pete Austin, Sougata Bose, Nicolas Mazzocchi, and Patrick Totzke

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

Abstract
Temporal graphs extend ordinary graphs with discrete time that affects the availability of edges. We consider solving games played on temporal graphs where one player aims to explore the graph, i.e., visit all vertices. The complexity depends majorly on two factors: the presence of an adversary and how edge availability is specified. We demonstrate that on static graphs, where edges are always available, solving explorability games is just as hard as solving reachability games. In contrast, on temporal graphs, the complexity of explorability coincides with generalized reachability (NP-complete for one-player and PSPACE-complete for two player games). We show that if temporal graphs are given symbolically, even one-player reachability (and thus explorability and generalized reachability) games are PSPACE-hard. For one player, all these are also solvable in PSPACE and for two players, they are in PSPACE, EXP and EXP, respectively.
Cite as

Pete Austin, Sougata Bose, Nicolas Mazzocchi, and Patrick Totzke. Temporal Explorability Games. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{austin_et_al:LIPIcs.CONCUR.2025.7,
  author =	{Austin, Pete and Bose, Sougata and Mazzocchi, Nicolas and Totzke, Patrick},
  title =	{{Temporal Explorability Games}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{7:1--7:17},
  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.2025.7},
  URN =		{urn:nbn:de:0030-drops-239575},
  doi =		{10.4230/LIPIcs.CONCUR.2025.7},
  annote =	{Keywords: Temporal Graphs, Explorability, Reachability, Games}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.138
Taming Infinity One Chunk at a Time: Concisely Represented Strategies in One-Counter MDPs

Authors: Michal Ajdarów, James C. A. Main, Petr Novotný, and Mickael Randour

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

Abstract
Markov decision processes (MDPs) are a canonical model to reason about decision making within a stochastic environment. We study a fundamental class of infinite MDPs: one-counter MDPs (OC-MDPs). They extend finite MDPs via an associated counter taking natural values, thus inducing an infinite MDP over the set of configurations (current state and counter value). We consider two characteristic objectives: reaching a target state (state-reachability), and reaching a target state with counter value zero (selective termination). The synthesis problem for the latter is not known to be decidable and connected to major open problems in number theory. Furthermore, even seemingly simple strategies (e.g., memoryless ones) in OC-MDPs might be impossible to build in practice (due to the underlying infinite configuration space): we need finite, and preferably small, representations. To overcome these obstacles, we introduce two natural classes of concisely represented strategies based on a (possibly infinite) partition of counter values in intervals. For both classes, and both objectives, we study the verification problem (does a given strategy ensure a high enough probability for the objective?), and two synthesis problems (does there exist such a strategy?): one where the interval partition is fixed as input, and one where it is only parameterized. We develop a generic approach based on a compression of the induced infinite MDP that yields decidability in all cases, with all complexities within PSPACE.
Cite as

Michal Ajdarów, James C. A. Main, Petr Novotný, and Mickael Randour. Taming Infinity One Chunk at a Time: Concisely Represented Strategies in One-Counter MDPs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 138:1-138:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ajdarow_et_al:LIPIcs.ICALP.2025.138,
  author =	{Ajdar\'{o}w, Michal and Main, James C. A. and Novotn\'{y}, Petr and Randour, Mickael},
  title =	{{Taming Infinity One Chunk at a Time: Concisely Represented Strategies in One-Counter MDPs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{138:1--138:19},
  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.2025.138},
  URN =		{urn:nbn:de:0030-drops-235157},
  doi =		{10.4230/LIPIcs.ICALP.2025.138},
  annote =	{Keywords: one-counter Markov decision processes, randomised strategies, termination, reachability}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.149
The Memory of ω-Regular and BC(Σ⁰₂) Objectives

Authors: Antonio Casares and Pierre Ohlmann

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

Abstract
In the context of 2-player zero-sum infinite duration games played on (potentially infinite) graphs, the memory of an objective is the smallest integer k such that in any game won by Eve, she has a strategy with ≤ k states of memory. For ω-regular objectives, checking whether the memory equals a given number k was not known to be decidable. In this work, we focus on objectives in BC(Σ⁰₂), i.e. recognised by a potentially infinite deterministic parity automaton. We provide a class of automata that recognise objectives with memory ≤ k, leading to the following results: - for ω-regular objectives, the memory can be computed in NP; - given two objectives W₁ and W₂ in BC(Σ⁰₂) and assuming W₁ is prefix-independent, the memory of W₁ ∪ W₂ is at most the product of the memories of W₁ and W₂. Our results also apply to chromatic memory, the variant where strategies can update their memory state only depending on which colour is seen.
Cite as

Antonio Casares and Pierre Ohlmann. The Memory of ω-Regular and BC(Σ⁰₂) Objectives. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 149:1-149:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{casares_et_al:LIPIcs.ICALP.2025.149,
  author =	{Casares, Antonio and Ohlmann, Pierre},
  title =	{{The Memory of \omega-Regular and BC(\Sigma⁰₂) Objectives}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{149:1--149:18},
  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.2025.149},
  URN =		{urn:nbn:de:0030-drops-235267},
  doi =		{10.4230/LIPIcs.ICALP.2025.149},
  annote =	{Keywords: Infinite duration games, Strategy complexity, Omega-regular}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.125
Unbalanced Random Matching Markets with Partial Preferences

Authors: Aditya Potukuchi and Shikha Singh

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

Abstract
Properties of stable matchings in the popular random-matching-market model have been studied for over 50 years. In a random matching market, each agent has complete preferences drawn uniformly and independently at random. Wilson (1972), Knuth (1976) and Pittel (1989) proved that in balanced random matching markets, the proposers are matched to their ln nth choice on average. In this paper, we consider competitive markets with n jobs and n+k candidates, and partial lists where each agent only ranks their top d choices. Despite the long history of the problem, the following fundamental question remains unanswered for these generalized markets: what is the tight threshold on list length d that results in a perfect stable matching with high probability? In this paper, we answer this question exactly - we prove a sharp threshold d₀ = ln n ⋅ ln (n+k)/(k+1) on the existence of perfect stable matchings when k = o(n). That is, we show that if d < (1-ε) d₀, then no stable matching matches all jobs; moreover, if d > (1+ ε) d₀, then all jobs are matched in every stable matching with high probability. This bound improves and generalizes recent results by Kanoria, Min and Qian (2021). Furthermore, we extend the line of work studying the effect of imbalance on the expected rank of the proposers (termed the "stark effect of competition"). We establish the regime in unbalanced markets that forces this stark effect to take shape in markets with partial preferences.
Cite as

Aditya Potukuchi and Shikha Singh. Unbalanced Random Matching Markets with Partial Preferences. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 125:1-125:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{potukuchi_et_al:LIPIcs.ICALP.2025.125,
  author =	{Potukuchi, Aditya and Singh, Shikha},
  title =	{{Unbalanced Random Matching Markets with Partial Preferences}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{125:1--125:16},
  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.2025.125},
  URN =		{urn:nbn:de:0030-drops-235025},
  doi =		{10.4230/LIPIcs.ICALP.2025.125},
  annote =	{Keywords: stable matching, probabilistic method, Gale-Shapley algorithm}
}
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