53 Search Results for "Colcombet, Thomas"

Document
DOI: 10.4230/LIPIcs.DISC.2025.18
Complexity Landscape for Local Certification

Authors: Nicolas Bousquet, Laurent Feuilloley, and Sébastien Zeitoun

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
An impressive recent line of work has charted the complexity landscape of distributed graph algorithms. For many settings, it has been determined which time complexities exist, and which do not (in the sense that no local problem could have an optimal algorithm with that complexity). In this paper, we initiate the study of the landscape for space complexity of distributed graph algorithms. More precisely, we focus on the local certification setting, where a prover assigns certificates to nodes to certify a property, and where the space complexity is measured by the size of the certificates. Already for anonymous paths and cycles, we unveil a surprising landscape: - There is a gap between complexity O(1) and Θ(log log n) in paths. This is the first gap established in local certification. - There exists a property that has complexity Θ(log log n) in paths, a regime that was not known to exist for a natural property. - There is a gap between complexity O(1) and Θ(log n) in cycles, hence a gap that is exponentially larger than for paths. We then generalize our result for paths to the class of trees. Namely, we show that there is a gap between complexity O(1) and Θ(log log d) in trees, where d is the diameter. We finally describe some settings where there are no gaps at all. To prove our results we develop a new toolkit, based on various results of automata theory and arithmetic, which is of independent interest.
Cite as

Nicolas Bousquet, Laurent Feuilloley, and Sébastien Zeitoun. Complexity Landscape for Local Certification. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 18:1-18:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bousquet_et_al:LIPIcs.DISC.2025.18,
  author =	{Bousquet, Nicolas and Feuilloley, Laurent and Zeitoun, S\'{e}bastien},
  title =	{{Complexity Landscape for Local Certification}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{18:1--18:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.18},
  URN =		{urn:nbn:de:0030-drops-248350},
  doi =		{10.4230/LIPIcs.DISC.2025.18},
  annote =	{Keywords: Local certification, proof-labeling schemes, locally checkable proofs, space complexity, distributed graph algorithms, complexity gap}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.50
Lexicographic Transductions of Finite Words

Authors: Emmanuel Filiot, Nathan Lhote, and Pierre-Alain Reynier

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

Abstract
Regular transductions over finite words have linear input-to-output growth. This class of transductions enjoys many characterizations, such as transductions computable by two-way transducers as well as transductions definable in MSO (in the sense of Courcelle). Recently, regular transductions have been extended by Bojańczyk to polyregular transductions, which have polynomial growth, and are characterized by pebble transducers and MSO interpretations. Another class of interest is that of transductions defined by streaming string transducers or marble transducers, which have exponential growth and are incomparable with polyregular transductions. In this paper, we consider MSO set interpretations (MSOSI) over finite words, that were introduced by Colcombet and Loeding. MSOSI are a natural candidate for the class of "regular transductions with exponential growth", and are rather well behaved. However, MSOSI for now lacks two desirable properties that regular and polyregular transductions have. The first property is to have an automata description. This property is closely related to a second property, that of being regularity preserving, meaning preserving regular languages under inverse image. We first show that if MSOSI are (effectively) regularity preserving then any automatic ω-word has a decidable MSO theory, an almost 20 years old conjecture of Bárány. Our main contribution is the introduction of a class of transductions of exponential growth, which we call lexicographic transductions. We provide three different presentations for this class: first, as the closure of simple transductions (recognizable transductions) under a single operator called maplex; second, as a syntactic fragment of MSOSI (but the regular languages are given by automata instead of formulas); and third, we give an automaton based model called nested marble transducers, which generalize both marble transducers and pebble transducers. We show that this class enjoys many nice properties including being regularity preserving.
Cite as

Emmanuel Filiot, Nathan Lhote, and Pierre-Alain Reynier. Lexicographic Transductions of Finite Words. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 50:1-50:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{filiot_et_al:LIPIcs.MFCS.2025.50,
  author =	{Filiot, Emmanuel and Lhote, Nathan and Reynier, Pierre-Alain},
  title =	{{Lexicographic Transductions of Finite Words}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{50:1--50:18},
  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.2025.50},
  URN =		{urn:nbn:de:0030-drops-241572},
  doi =		{10.4230/LIPIcs.MFCS.2025.50},
  annote =	{Keywords: Transducers, Automata, MSO, Logical interpretations, Automatic structures}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.64
Positional-Player Games

Authors: Orna Kupferman and Noam Shenwald

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

Abstract
In reactive synthesis, we transform a specification to a system that satisfies the specification in all environments. For specifications in linear-temporal logic, research on bounded synthesis, where the sizes of the system and the environment are bounded, captures realistic settings and has lead to algorithms of improved complexity and implementability. In the game-based {a}pproach to synthesis, the system and its environment are modeled by strategies in a two-player game with an ω-regular objective, induced by the specification. There, bounded synthesis corresponds to bounding the memory of the strategies of the players. The memory requirement for various objectives has been extensively studied. In particular, researchers have identified positional objectives, where the winning player can follow a memoryless strategy - one that needs no memory. In this work we study bounded synthesis in the game setting. Specifically, we define and study positional-player games, in which one or both players are restricted to memoryless strategies, which correspond to non-intrusive control in various applications. We study positional-player games with Rabin, Streett, and Muller objectives, as well as with weighted multiple Büchi and reachability objectives. Our contribution covers their theoretical properties as well as a complete picture of the complexity of deciding the game in the various settings.
Cite as

Orna Kupferman and Noam Shenwald. Positional-Player Games. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 64:1-64:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kupferman_et_al:LIPIcs.MFCS.2025.64,
  author =	{Kupferman, Orna and Shenwald, Noam},
  title =	{{Positional-Player Games}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{64:1--64:19},
  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.2025.64},
  URN =		{urn:nbn:de:0030-drops-241719},
  doi =		{10.4230/LIPIcs.MFCS.2025.64},
  annote =	{Keywords: Games, \omega-Regular Objectives, Memory, Complexity}
}
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.2025.70
Labelled Well Quasi Ordered Classes of Bounded Linear Clique-Width

Authors: Aliaume Lopez

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

Abstract
We construct an algorithm that inputs an MSO-interpretation from finite words to graphs, and decides if there exists a k ∈ ℕ such that the class of graphs induced by the interpretation is not well-quasi-ordered by the induced subgraph relation when vertices are freely labelled using {1, …, k}. In case no such k exists, we also prove that the class of graphs is not well-quasi-ordered by the induced subgraph relation when vertices are freely labelled using any well-quasi-ordered set of labels. As a byproduct of our analysis, we prove that for classes of bounded linear clique-width, a weak version of a conjecture by Pouzet holds.
Cite as

Aliaume Lopez. Labelled Well Quasi Ordered Classes of Bounded Linear Clique-Width. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 70:1-70:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lopez:LIPIcs.MFCS.2025.70,
  author =	{Lopez, Aliaume},
  title =	{{Labelled Well Quasi Ordered Classes of Bounded Linear Clique-Width}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{70:1--70:17},
  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.2025.70},
  URN =		{urn:nbn:de:0030-drops-241773},
  doi =		{10.4230/LIPIcs.MFCS.2025.70},
  annote =	{Keywords: well-quasi-ordering, linear clique-width, MSO transduction, automata theory}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.MFCS.2025.1
Lambdas, Transducers and MSO (Invited Talk)

Authors: Thomas Colcombet

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

Abstract
This talk will revolve around the classical question: What kind of maps from words to words or trees to trees can be considered as "well behaved" from an automata theoretic point of view? What means to be well-behaved is left unspecified on purpose, but one thing is sure is that one would expect as minimal requirement that the inverse image of a regular language under such a map be effectively regular. One would also expect to have nice closure properties for these maps, in particular under composition. Ideally, we would also like to have several different equivalent computation models for representing them. This talk advertises the use of simply-typed lambda calculus as a good way to approach this question, and presents newer results concerning translations from and to exponential growth maps. This line of research is rooted in a long literature, starting from the works of Damm on higher order grammars, and the works of Engelfriet and Vogler on macro-tree transducers, and more generally from works on higher-order tree transducers, as well as the results of Ong et al. on decidability of MSO over higher-order recursion schemes (a model that produces infinite trees). These works show in a broad sense that models of computation defined in simply typed lambda-calculus do preserve regularity under taking the inverse image. Another connection is the recent implicit automata research programme initiated by Nguy~ên and Pradic, that was inspired by the seminal work of Hillebrand and Kanellakis. Here, automata models a directly viewed as programs written in some form of typed lambda-calculus, using Church encoding for representing inputs and outputs. When appropriately controlling the type system various it is possible to characterize various classes of finite state transducers studied in the literature. A last approach comes from finite model-theory. In this context, Monadic Second-Order Logic (MSO for short, the extension of first-order in which one can further quantify over sets) is the prime logic for describing regular languages over words or trees. This logic can also be used for defining transformations from words/trees to words/trees. These are the notions of MSO-interpretations or MSO-transducers. A major contribution here is the study of the expressive power of MSO-interpretations of polynomial growth from words to words that was undertaken by Bojańczyk, Kiefer and Lhote, and shown equivalent to other formalisms of transducers and programming languages. This is the class of polyregular functions, and it satisfies all the expectation of the question. Yet it is limited to finite words as inputs and outputs, and to polynomial growth. In a first part of the talk, we shall see how to use simply-typed lambda-calculus as a general mechanism for transforming trees into trees, and how it gives a positive answer to the original question. This description essentially repackages many ideas existing from the literature, in a way similar Gallot’s thesis. It also introduces a few new ones. In particular, we shall see generic results that some clearly identified classes of functional programs describing transformations from trees to trees can be effectively compiled into transducer-like models which perform only one pass on the input (i.e. higher-order tree transducers). This class of programs is also closed under composition. We shall also see how the logic MSO itself can be natively embedded in such models of computation. In a second part, we will see how this presentation relates to recent works with Lhote, Nguy~ên and Ohlmann in which extensions of polyregular functions to maps from words to words of exponential growth are studied. This work has the particularity to be the first one in the model-theoretic side of this theory in which it is key to allow lambda-terms to be unsafe.
Cite as

Thomas Colcombet. Lambdas, Transducers and MSO (Invited Talk). In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{colcombet:LIPIcs.MFCS.2025.1,
  author =	{Colcombet, Thomas},
  title =	{{Lambdas, Transducers and MSO}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{1:1--1:1},
  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.2025.1},
  URN =		{urn:nbn:de:0030-drops-241087},
  doi =		{10.4230/LIPIcs.MFCS.2025.1},
  annote =	{Keywords: Lambda-calculus, automata theory, finite model theory, MSO}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.13
Languages of Boundedly-Ambiguous Vector Addition Systems with States

Authors: Wojciech Czerwiński and Łukasz Orlikowski

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

Abstract
The aim of this paper is to deliver broad understanding of a class of languages of boundedly-ambiguous VASSs, that is k-ambiguous VASSs for some natural k. These are languages of Vector Addition Systems with States with the acceptance condition defined by the set of accepting states such that each accepted word has at most k accepting runs. We develop tools for proving that a given language is not accepted by any k-ambiguous VASS. Using them we show a few negative results: lack of some closure properties of languages of k-ambiguous VASSs and undecidability of the k-ambiguity problem, namely the question whether a given VASS language is a language of some k-ambiguous VASS. In fact we show an even more general undecidability result stating that for any class containing all regular languages and only k-ambiguous VASS languages for some k ∈ ℕ it is undecidable whether a language of a given 1-dimensional VASS belongs to this class. Finally, we show that the regularity problem is decidable for k-ambiguous VASSs.
Cite as

Wojciech Czerwiński and Łukasz Orlikowski. Languages of Boundedly-Ambiguous Vector Addition Systems with States. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 13:1-13:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{czerwinski_et_al:LIPIcs.CONCUR.2025.13,
  author =	{Czerwi\'{n}ski, Wojciech and Orlikowski, {\L}ukasz},
  title =	{{Languages of Boundedly-Ambiguous Vector Addition Systems with States}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{13:1--13:23},
  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.2025.13},
  URN =		{urn:nbn:de:0030-drops-239635},
  doi =		{10.4230/LIPIcs.CONCUR.2025.13},
  annote =	{Keywords: vector addition systems, Petri nets, unambiguity, bounded-ambiguity, languages}
}
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
(Co)algebraic pearl
DOI: 10.4230/LIPIcs.CALCO.2025.16
Active Learning of Upward-Closed Sets of Words ((Co)algebraic pearl)

Authors: Quentin Aristote

Published in: LIPIcs, Volume 342, 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)

Abstract
We give a new proof of a result from well quasi-order theory on the computability of bases for upwards-closed sets of words. This new proof is based on Angluin’s L* algorithm, that learns an automaton from a minimally adequate teacher. This relates in particular two results from the 1980s: Angluin’s L* algorithm, and a result from Valk and Jantzen on the computability of bases for upwards-closed sets of tuples of integers. Along the way, we describe an algorithm for learning quasi-ordered automata from a minimally adequate teacher, and extend a generalization of Valk and Jantzen’s result, encompassing both words and integers, to finitely generated monoids.
Cite as

Quentin Aristote. Active Learning of Upward-Closed Sets of Words ((Co)algebraic pearl). In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 16:1-16:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aristote:LIPIcs.CALCO.2025.16,
  author =	{Aristote, Quentin},
  title =	{{Active Learning of Upward-Closed Sets of Words}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{16:1--16:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-383-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{342},
  editor =	{C\^{i}rstea, Corina and Knapp, Alexander},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2025.16},
  URN =		{urn:nbn:de:0030-drops-235751},
  doi =		{10.4230/LIPIcs.CALCO.2025.16},
  annote =	{Keywords: active learning, well quasi-orders, Valk-Jantzen lemma, piecewise-testable languages, monoids}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.152
Tree Algebras and Bisimulation-Invariant MSO on Finite Graphs

Authors: Thomas Colcombet, Amina Doumane, and Denis Kuperberg

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

Abstract
We establish that the bisimulation invariant fragment of MSO over finite transition systems is expressively equivalent over finite transition systems to modal μ-calculus, a question that had remained open for several decades. The proof goes by translating the question to an algebraic framework, and showing that the languages of regular trees that are recognised by finitary tree algebras whose sorts zero and one are finite are the regular ones. This corresponds for trees to a weak form of the key translation of Wilke algebras to omega-semigroup over infinite words, and was also a missing piece in the algebraic theory of regular languages of infinite trees for twenty years.
Cite as

Thomas Colcombet, Amina Doumane, and Denis Kuperberg. Tree Algebras and Bisimulation-Invariant MSO on Finite Graphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 152:1-152:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{colcombet_et_al:LIPIcs.ICALP.2025.152,
  author =	{Colcombet, Thomas and Doumane, Amina and Kuperberg, Denis},
  title =	{{Tree Algebras and Bisimulation-Invariant MSO on Finite Graphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{152:1--152:16},
  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.2025.152},
  URN =		{urn:nbn:de:0030-drops-235294},
  doi =		{10.4230/LIPIcs.ICALP.2025.152},
  annote =	{Keywords: MSO, mu-calculus, finite graphs, bisimulation, tree algebra}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.165
Algebraic Language Theory with Effects

Authors: Fabian Lenke, Stefan Milius, Henning Urbat, and Thorsten Wißmann

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

Abstract
Regular languages - the languages accepted by deterministic finite automata - are known to be precisely the languages recognized by finite monoids. This characterization is the origin of algebraic language theory. In this paper, we generalize the correspondence between automata and monoids to automata with generic computational effects given by a monad, providing the foundations of an effectful algebraic language theory. We show that, under suitable conditions on the monad, a language is computable by an effectful automaton precisely when it is recognizable by (1) an effectful monoid morphism into an effect-free finite monoid, and (2) a monoid morphism into a monad-monoid bialgebra whose carrier is a finitely generated algebra for the monad, the former mode of recognition being conceptually completely new. Our prime application is a novel algebraic approach to languages computed by probabilistic finite automata. Additionally, we derive new algebraic characterizations for nondeterministic probabilistic finite automata and for weighted finite automata over unrestricted semirings, generalizing previous results on weighted algebraic recognition over commutative rings.
Cite as

Fabian Lenke, Stefan Milius, Henning Urbat, and Thorsten Wißmann. Algebraic Language Theory with Effects. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 165:1-165:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lenke_et_al:LIPIcs.ICALP.2025.165,
  author =	{Lenke, Fabian and Milius, Stefan and Urbat, Henning and Wi{\ss}mann, Thorsten},
  title =	{{Algebraic Language Theory with Effects}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{165:1--165:20},
  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.2025.165},
  URN =		{urn:nbn:de:0030-drops-235423},
  doi =		{10.4230/LIPIcs.ICALP.2025.165},
  annote =	{Keywords: Automaton, Monoid, Monad, Effect, Algebraic language theory}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.160
Using Games and Universal Trees to Characterise the Nondeterministic Index of Tree Languages

Authors: Olivier Idir and Karoliina Lehtinen

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

Abstract
The parity index problem of tree automata asks, given a regular tree language L and a set of priorities J, is L J-feasible, that is, recognised by a nondeterministic parity automaton with priorities J? This is a long-standing open problem, of which only a few sub-cases and variations are known to be decidable. In a significant but technically difficult step, Colcombet and Löding reduced the problem to the uniform universality of distance-parity automata. In this article, we revisit the index problem using tools from the parity game literature. We add some counters to Lehtinen’s register game, originally used to solve parity games in quasipolynomial time, and use this novel game to characterise J-feasibility. This provides a alternative proof to Colcombet and Löding’s reduction. We then provide a second characterisation, based on the notion of attractor decompositions and the complexity of their structure, as measured by a parameterised version of their Strahler number, which we call n-Strahler number. Finally, we rephrase this result using the notion of universal tree extended to automata: a guidable automaton recognises a [1,2j]-feasible language if and only if it admits a universal tree with n-Strahler number j, for some n. In particular, a language recognised by a guidable automaton {A} is Büchi-feasible if and only if there is a uniform bound n ∈ ℕ such that all trees in the language admit an accepting run with an attractor decomposition of width bounded by n. Equivalently, the language is Büchi-feasible if and only if {A} admits a finite universal tree. While we do not solve the decidability of the index problem, our work makes the state-of-the-art more accessible and brings to light the deep relationships between the J-feasibility of a language and attractor decompositions, universal trees and Lehtinen’s register game.
Cite as

Olivier Idir and Karoliina Lehtinen. Using Games and Universal Trees to Characterise the Nondeterministic Index of Tree Languages. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 160:1-160:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{idir_et_al:LIPIcs.ICALP.2025.160,
  author =	{Idir, Olivier and Lehtinen, Karoliina},
  title =	{{Using Games and Universal Trees to Characterise the Nondeterministic Index of Tree Languages}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{160:1--160:19},
  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.2025.160},
  URN =		{urn:nbn:de:0030-drops-235377},
  doi =		{10.4230/LIPIcs.ICALP.2025.160},
  annote =	{Keywords: Tree automata, parity automata, Mostowski index, Strahler number, attractor decomposition, universal trees}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.162
Positive and Monotone Fragments of FO and LTL

Authors: Simon Iosti, Denis Kuperberg, and Quentin Moreau

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

Abstract
We study the positive logic FO^+ on finite words, and its fragments, pursuing and refining the work initiated in [Denis Kuperberg, 2023]. First, we transpose notorious logic equivalences into positive first-order logic: FO^+ is equivalent to LTL^+, and its two-variable fragment FO^{2+} with (resp. without) successor available is equivalent to UTL^+ with (resp. without) the "next" operator X available. This shows that despite previous negative results, the class of FO^+-definable languages exhibits some form of robustness. We then exhibit an example of an FO-definable monotone language on one predicate, that is not FO^+-definable, refining the example from [Denis Kuperberg, 2023] with 3 predicates. Moreover, we show that such a counter-example cannot be FO²-definable. Finally, we provide a new example distinguishing the positive and monotone versions of FO² without quantifier alternation. This does not rely on a variant of the previously known counter-example, and witnesses a new phenomenon.
Cite as

Simon Iosti, Denis Kuperberg, and Quentin Moreau. Positive and Monotone Fragments of FO and LTL. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 162:1-162:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{iosti_et_al:LIPIcs.ICALP.2025.162,
  author =	{Iosti, Simon and Kuperberg, Denis and Moreau, Quentin},
  title =	{{Positive and Monotone Fragments of FO and LTL}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{162:1--162:17},
  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.2025.162},
  URN =		{urn:nbn:de:0030-drops-235398},
  doi =		{10.4230/LIPIcs.ICALP.2025.162},
  annote =	{Keywords: Positive logic, LTL, separation, first-order, monotone}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.154
Submonoid Membership in n-Dimensional Lamplighter Groups and S-Unit Equations

Authors: Ruiwen Dong

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

Abstract
We show that Submonoid Membership is decidable in n-dimensional lamplighter groups (ℤ/pℤ) ≀ ℤⁿ for any prime p and integer n. More generally, we show decidability of Submonoid Membership in semidirect products of the form 𝒴 ⋊ ℤⁿ, where 𝒴 is any finitely presented module over the Laurent polynomial ring 𝔽_p[X₁^{±}, …, X_n^{±}]. Combined with a result of Shafrir (2024), this gives the first example of a group G and a finite index subgroup G̃ ≤ G, such that Submonoid Membership is decidable in G̃ but undecidable in G. To obtain our decidability result, we reduce Submonoid Membership in 𝒴 ⋊ ℤⁿ to solving S-unit equations over 𝔽_p[X₁^{±}, …, X_n^{±}]-modules. We show that the solution set of such equations is effectively p-automatic, extending a result of Adamczewski and Bell (2012). As an intermediate result, we also obtain that the solution set of the Knapsack Problem in 𝒴 ⋊ ℤⁿ is effectively p-automatic.
Cite as

Ruiwen Dong. Submonoid Membership in n-Dimensional Lamplighter Groups and S-Unit Equations. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 154:1-154:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dong:LIPIcs.ICALP.2025.154,
  author =	{Dong, Ruiwen},
  title =	{{Submonoid Membership in n-Dimensional Lamplighter Groups and S-Unit Equations}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{154:1--154:20},
  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.2025.154},
  URN =		{urn:nbn:de:0030-drops-235316},
  doi =		{10.4230/LIPIcs.ICALP.2025.154},
  annote =	{Keywords: Submonoid Membership, lamplighter groups, S-unit equations, p-automatic sets, Knapsack in groups}
}
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}
}
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