DROPS

Document

DOI: 10.4230/LIPIcs.CSL.2026.30

Reward Interfaces with Best-Effort Implementations

Authors: Rafael Dewes and Rayna Dimitrova

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract

Interface theories, notably interface automata, serve as expressive frameworks for component-based design, specifying component behavior and interaction in concurrent systems. Traditional interface formalisms specify assumptions that a component’s environment must satisfy and the guarantees that each component provides. This qualitative view of component interaction based on imposing strict assumptions and Boolean guarantees may, however, not be expressive enough to capture the system’s allowed or desired behaviors under different environments. In this paper, we introduce reward interfaces to support component-based design while accommodating multi-valued correctness requirements and adaptive best-effort satisfaction of component’s guarantees. Building upon interface automata, our framework enables modeling a rich class of quantitative component specifications. We propose formal notions of implementation, refinement and compatibility for reward interfaces. We study a class of reward interfaces with automata-based representations, for which we provide algorithms for checking compatibility and refinement, and existence of best-effort implementations. Our framework offers a comprehensive approach to reward interface specification and design.

Cite as

Rafael Dewes and Rayna Dimitrova. Reward Interfaces with Best-Effort Implementations. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 30:1-30:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dewes_et_al:LIPIcs.CSL.2026.30,
  author =	{Dewes, Rafael and Dimitrova, Rayna},
  title =	{{Reward Interfaces with Best-Effort Implementations}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{30:1--30:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.30},
  URN =		{urn:nbn:de:0030-drops-254553},
  doi =		{10.4230/LIPIcs.CSL.2026.30},
  annote =	{Keywords: Component-based design, interface automata, quantitative specifications}
}

Document

DOI: 10.4230/LIPIcs.CSL.2026.45

Reasoning About Quality in Hyperproperties

Authors: Samuel Graepler, Benjamin Monmege, and Jean-Marc Talbot

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract

Hyperproperties allow one to specify properties of systems that inherently involve not single executions of the system, but several of them at once: observational determinism and non-inference are two examples of such properties used to study the security of systems. Logics like HyperLTL have been studied in the past to model check hyperproperties of systems. However, most of the time, requiring strict security properties is actually ineffective as systems do not meet such requirements. To overcome this issue, we introduce qualitative reasoning in HyperLTL, inspired by a similar work on LTL by Almagor, Boker and Kupferman [Almagor et al., 2016] where a formula has a value in the interval [0, 1], obtained by considering either a propositional quality (how much the specification is satisfied), or a temporal quality (when the specification is satisfied). We show decidability of the approximated model checking problem, as well as the model checking of large fragments.

Cite as

Samuel Graepler, Benjamin Monmege, and Jean-Marc Talbot. Reasoning About Quality in Hyperproperties. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 45:1-45:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{graepler_et_al:LIPIcs.CSL.2026.45,
  author =	{Graepler, Samuel and Monmege, Benjamin and Talbot, Jean-Marc},
  title =	{{Reasoning About Quality in Hyperproperties}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{45:1--45:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.45},
  URN =		{urn:nbn:de:0030-drops-254704},
  doi =		{10.4230/LIPIcs.CSL.2026.45},
  annote =	{Keywords: Hyperlogics, Automata-based model checking, Quantitative verification}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2025.57

Resolving Nondeterminism with Randomness

Authors: Thomas A. Henzinger, Aditya 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, Aditya 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, Aditya 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.CONCUR.2025.21

Quantitative Language Automata

Authors: Thomas A. Henzinger, Pavol Kebis, Nicolas Mazzocchi, and N. Ege Saraç

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

Abstract

A quantitative word automaton (QWA) defines a function from infinite words to values. For example, every infinite run of a limit-average QWA 𝒜 obtains a mean payoff, and every word w ∈ Σ^ω is assigned the maximal mean payoff obtained by nondeterministic runs of 𝒜 over w. We introduce quantitative language automata (QLAs) that define functions from language generators (i.e., implementations) to values, where a language generator can be nonprobabilistic, defining a set of infinite words, or probabilistic, defining a probability measure over infinite words. A QLA consists of a QWA and an aggregator function. For example, given a QWA 𝒜, the infimum aggregator maps each language L ⊆ Σ^ω to the greatest lower bound assigned by 𝒜 to any word in L. For boolean value sets, QWAs define boolean properties of traces, and QLAs define boolean properties of sets of traces, i.e., hyperproperties. For more general value sets, QLAs serve as a specification language for a generalization of hyperproperties, called quantitative hyperproperties. A nonprobabilistic (resp. probabilistic) quantitative hyperproperty assigns a value to each set (resp. distribution) G of traces, e.g., the minimal (resp. expected) average response time exhibited by the traces in G. We give several examples of quantitative hyperproperties and investigate three paradigmatic problems for QLAs: evaluation, nonemptiness, and universality. In the evaluation problem, given a QLA 𝔸 and an implementation G, we ask for the value that 𝔸 assigns to G. In the nonemptiness (resp. universality) problem, given a QLA 𝔸 and a value k, we ask whether 𝔸 assigns at least k to some (resp. every) language. We provide a comprehensive picture of decidability for these problems for QLAs with common aggregators as well as their restrictions to ω-regular languages and trace distributions generated by finite-state Markov chains.

Cite as

Thomas A. Henzinger, Pavol Kebis, Nicolas Mazzocchi, and N. Ege Saraç. Quantitative Language Automata. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 21:1-21:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{henzinger_et_al:LIPIcs.CONCUR.2025.21,
  author =	{Henzinger, Thomas A. and Kebis, Pavol and Mazzocchi, Nicolas and Sara\c{c}, N. Ege},
  title =	{{Quantitative Language Automata}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{21:1--21:24},
  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.2025.21},
  URN =		{urn:nbn:de:0030-drops-239718},
  doi =		{10.4230/LIPIcs.CONCUR.2025.21},
  annote =	{Keywords: Quantitative hyperproperties, quantitative automata, automata-based verification}
}

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.2025.155

Approximate Problems for Finite Transducers

Authors: Emmanuel Filiot, Ismaël Jecker, Khushraj Madnani, and Saina Sunny

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

Abstract

Finite (word) state transducers extend finite state automata by defining a binary relation over finite words, called rational relation. If the rational relation is the graph of a function, this function is said to be rational. The class of sequential functions is a strict subclass of rational functions, defined as the functions recognised by input-deterministic finite state transducers. The class membership problems between those classes are known to be decidable. We consider approximate versions of these problems and show they are decidable as well. This includes the approximate functionality problem, which asks whether given a rational relation (by a transducer), is it close to a rational function, and the approximate determinisation problem, which asks whether a given rational function is close to a sequential function. We prove decidability results for several classical distances, including Hamming and Levenshtein edit distance. Finally, we investigate the approximate uniformisation problem, which asks, given a rational relation R, whether there exists a sequential function that is close to some function uniformising R. As its exact version, we prove that this problem is undecidable.

Cite as

Emmanuel Filiot, Ismaël Jecker, Khushraj Madnani, and Saina Sunny. Approximate Problems for Finite Transducers. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 155:1-155:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{filiot_et_al:LIPIcs.ICALP.2025.155,
  author =	{Filiot, Emmanuel and Jecker, Isma\"{e}l and Madnani, Khushraj and Sunny, Saina},
  title =	{{Approximate Problems for Finite Transducers}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{155:1--155:19},
  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.2025.155},
  URN =		{urn:nbn:de:0030-drops-235329},
  doi =		{10.4230/LIPIcs.ICALP.2025.155},
  annote =	{Keywords: Finite state transducers, Edit distance, Determinisation, Functionality}
}

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 B: Automata, Logic, Semantics, and Theory of Programming

DOI: 10.4230/LIPIcs.ICALP.2025.145

Reducing Stochastic Games to Semidefinite Programming

Authors: Manuel Bodirsky, Georg Loho, and Mateusz Skomra

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

Abstract

We present a polynomial-time reduction from max-average constraints to the feasibility problem for semidefinite programs. This shows that Condon’s simple stochastic games, stochastic mean payoff games, and in particular mean payoff games and parity games can all be reduced to semidefinite programming.

Cite as

Manuel Bodirsky, Georg Loho, and Mateusz Skomra. Reducing Stochastic Games to Semidefinite Programming. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 145:1-145:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bodirsky_et_al:LIPIcs.ICALP.2025.145,
  author =	{Bodirsky, Manuel and Loho, Georg and Skomra, Mateusz},
  title =	{{Reducing Stochastic Games to Semidefinite Programming}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{145:1--145:15},
  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.2025.145},
  URN =		{urn:nbn:de:0030-drops-235224},
  doi =		{10.4230/LIPIcs.ICALP.2025.145},
  annote =	{Keywords: Mean-payoff games, stochastic games, semidefinite programming, max-average constraints, max-atom problem}
}

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

DOI: 10.4230/LIPIcs.ICALP.2025.146

Saturation Problems for Families of Automata

Authors: León Bohn, Yong Li, Christof Löding, and Sven Schewe

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

Abstract

Families of deterministic finite automata (FDFA) represent regular ω-languages through their ultimately periodic words (UP-words). An FDFA accepts pairs of words, where the first component corresponds to a prefix of the UP-word, and the second component represents a period of that UP-word. An FDFA is termed saturated if, for each UP-word, either all or none of the pairs representing that UP-word are accepted. We demonstrate that determining whether a given FDFA is saturated can be accomplished in polynomial time, thus improving the known PSPACE upper bound by an exponential. We illustrate the application of this result by presenting the first polynomial learning algorithms for representations of the class of all regular ω-languages. Furthermore, we establish that deciding a weaker property, referred to as almost saturation, is PSPACE-complete. Since FDFAs do not necessarily define regular ω-languages when they are not saturated, we also address the regularity problem and show that it is PSPACE-complete. Finally, we explore a variant of FDFAs called families of deterministic weak automata (FDWA), where the semantics for the periodic part of the UP-word considers ω-words instead of finite words. We demonstrate that saturation for FDWAs is also decidable in polynomial time, that FDWAs always define regular ω-languages, and we compare the succinctness of these different models.

Cite as

León Bohn, Yong Li, Christof Löding, and Sven Schewe. Saturation Problems for Families of Automata. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 146:1-146:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bohn_et_al:LIPIcs.ICALP.2025.146,
  author =	{Bohn, Le\'{o}n and Li, Yong and L\"{o}ding, Christof and Schewe, Sven},
  title =	{{Saturation Problems for Families of Automata}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{146:1--146:19},
  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.2025.146},
  URN =		{urn:nbn:de:0030-drops-235239},
  doi =		{10.4230/LIPIcs.ICALP.2025.146},
  annote =	{Keywords: Families of Automata, automata learning, FDFAs}
}

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.CSL.2025.22

On the Minimisation of Deterministic and History-Deterministic Generalised (Co)Büchi Automata

Authors: Antonio Casares, Olivier Idir, Denis Kuperberg, Corto Mascle, and Aditya Prakash

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

Abstract

We present a polynomial-time algorithm minimising the number of states of history-deterministic generalised coBüchi automata, building on the work of Abu Radi and Kupferman on coBüchi automata. On the other hand, we establish that the minimisation problem for both deterministic and history-deterministic generalised Büchi automata is NP-complete, as well as the problem of minimising at the same time the number of states and colours of history-deterministic generalised coBüchi automata.

Cite as

Antonio Casares, Olivier Idir, Denis Kuperberg, Corto Mascle, and Aditya Prakash. On the Minimisation of Deterministic and History-Deterministic Generalised (Co)Büchi Automata. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 22:1-22:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{casares_et_al:LIPIcs.CSL.2025.22,
  author =	{Casares, Antonio and Idir, Olivier and Kuperberg, Denis and Mascle, Corto and Prakash, Aditya},
  title =	{{On the Minimisation of Deterministic and History-Deterministic Generalised (Co)B\"{u}chi Automata}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{22:1--22:18},
  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.2025.22},
  URN =		{urn:nbn:de:0030-drops-227798},
  doi =		{10.4230/LIPIcs.CSL.2025.22},
  annote =	{Keywords: Automata minimisation, omega-regular languages, good-for-games automata}
}

Document

DOI: 10.4230/LIPIcs.CSL.2025.19

Two-Way One-Counter Nets Revisited

Authors: Shaull Almagor, Michaël Cadilhac, and Asaf Yeshurun

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

Abstract

One Counter Nets (OCNs) are finite-state automata equipped with a counter that cannot become negative, but cannot be explicitly tested for zero. Their close connection to various other models (e.g., PDAs, Vector Addition Systems, and Counter Automata) make them an attractive modeling tool. The two-way variant of OCNs (2-OCNs) was introduced in the 1980’s and shown to be more expressive than OCNs, so much so that the emptiness problem is undecidable already in the deterministic model (2-DOCNs). In a first part, we study the emptiness problem of natural restrictions of 2-OCNs, under the light of modern results about Vector Addition System with States (VASS). We show that emptiness is decidable for 2-OCNs over bounded languages (i.e., languages contained in a₁^* a₂^* ⋯ a_k^*), and decidable and Ackermann-complete for sweeping 2-OCNs, where the head direction only changes at the end-markers. Both decidability results revolve around reducing the problem to VASS reachability, but they rely on strikingly different approaches. In a second part, we study the expressive power of 2-OCNs, showing an array of connections between bounded languages, sweeping 2-OCNs, and semilinear languages. Most noteworthy among these connections, is that the bounded languages recognized by sweeping 2-OCNs are precisely those that are semilinear. Finally, we establish an intricate pumping lemma for 2-DOCNs and use it to show that there are OCN languages that are not 2-DOCN recognizable, improving on the known result that there are such 2-OCN languages.

Cite as

Shaull Almagor, Michaël Cadilhac, and Asaf Yeshurun. Two-Way One-Counter Nets Revisited. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 19:1-19:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{almagor_et_al:LIPIcs.CSL.2025.19,
  author =	{Almagor, Shaull and Cadilhac, Micha\"{e}l and Yeshurun, Asaf},
  title =	{{Two-Way One-Counter Nets Revisited}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{19:1--19:20},
  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.2025.19},
  URN =		{urn:nbn:de:0030-drops-227765},
  doi =		{10.4230/LIPIcs.CSL.2025.19},
  annote =	{Keywords: Counter Net, Two way, Automata}
}

Document

DOI: 10.4230/LIPIcs.CONCUR.2024.12

History-Determinism vs Fair Simulation

Authors: Udi Boker, Thomas A. Henzinger, Karoliina Lehtinen, and Aditya Prakash

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract

An automaton 𝒜 is history-deterministic if its nondeterminism can be resolved on the fly, only using the prefix of the word read so far. This mild form of nondeterminism has attracted particular attention for its applications in synthesis problems. An automaton 𝒜 is guidable with respect to a class C of automata if it can fairly simulate every automaton in C, whose language is contained in that of 𝒜. In other words, guidable automata are those for which inclusion and simulation coincide, making them particularly interesting for model-checking. We study the connection between these two notions, and specifically the question of when they coincide. For classes of automata on which they do, deciding guidability, an otherwise challenging decision problem, reduces to deciding history-determinism, a problem that is starting to be well-understood for many classes. We provide a selection of sufficient criteria for a class of automata to guarantee the coincidence of the notions, and use them to show that the notions coincide for the most common automata classes, among which are ω-regular automata and many infinite-state automata with safety and reachability acceptance conditions, including vector addition systems with states, one-counter nets, pushdown-, Parikh-, and timed-automata. We also demonstrate that history-determinism and guidability do not always coincide, for example, for the classes of timed automata with a fixed number of clocks.

Cite as

Udi Boker, Thomas A. Henzinger, Karoliina Lehtinen, and Aditya Prakash. History-Determinism vs Fair Simulation. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{boker_et_al:LIPIcs.CONCUR.2024.12,
  author =	{Boker, Udi and Henzinger, Thomas A. and Lehtinen, Karoliina and Prakash, Aditya},
  title =	{{History-Determinism vs Fair Simulation}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{12:1--12:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak 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.CONCUR.2024.12},
  URN =		{urn:nbn:de:0030-drops-207841},
  doi =		{10.4230/LIPIcs.CONCUR.2024.12},
  annote =	{Keywords: History-Determinism}
}

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

DOI: 10.4230/LIPIcs.ICALP.2024.124

Lookahead Games and Efficient Determinisation of History-Deterministic Büchi Automata

Authors: Rohan Acharya, Marcin Jurdziński, and Aditya Prakash

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract

Our main technical contribution is a polynomial-time determinisation procedure for history-deterministic Büchi automata, which settles an open question of Kuperberg and Skrzypczak, 2015. A key conceptual contribution is the lookahead game, which is a variant of Bagnol and Kuperberg’s token game, in which Adam is given a fixed lookahead. We prove that the lookahead game is equivalent to the 1-token game. This allows us to show that the 1-token game characterises history-determinism for semantically-deterministic Büchi automata, which paves the way to our polynomial-time determinisation procedure.

Cite as

Rohan Acharya, Marcin Jurdziński, and Aditya Prakash. Lookahead Games and Efficient Determinisation of History-Deterministic Büchi Automata. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 124:1-124:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{acharya_et_al:LIPIcs.ICALP.2024.124,
  author =	{Acharya, Rohan and Jurdzi\'{n}ski, Marcin and Prakash, Aditya},
  title =	{{Lookahead Games and Efficient Determinisation of History-Deterministic B\"{u}chi Automata}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{124:1--124:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.124},
  URN =		{urn:nbn:de:0030-drops-202672},
  doi =		{10.4230/LIPIcs.ICALP.2024.124},
  annote =	{Keywords: History determinism, Good-for-games, Automata over infinite words, Games}
}

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