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Documents authored by Cadilhac, Michaël

Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2026.163
Shuffles of Context-Free Languages Along Regular Trajectories

Authors: Corentin Barloy, Michaël Cadilhac, and Kyle Ockerlund

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

Abstract
In single-core processors, concurrency requires that multiple processes be interleaved into a single thread of execution by a scheduler. The language-theoretic operation that corresponds to this is the shuffle of two languages: the set of words obtained by interleaving a word from each language in an arbitrary, letter-wise fashion. It is well known that regular languages are closed under shuffles, while context-free languages (CFLs) are not. Following an established line of research, this paper considers shuffles according to regular "trajectories," that is, subject to scheduling constraints expressed by an automaton. Unsurprisingly, some trajectories allow for CFLs to be shuffled into CFLs (e.g., simple concatenation of the two words), while others do not. This paper provides a robust toolset to show that a given trajectory would always shuffle two nonregular CFLs into a nonCFL. In the case of deterministic CFLs (DCFLs), a salient trichotomy of trajectories depending on how they shuffle DCFLs is provided. These results are based on lemmata of independent interest regarding how pushdown automata (PDA) must invoke the stack when accepting a nonregular CFL or DCFL. The latter case relies on a recent result of Jančar and Šíma (MFCS'2021); answering an open question therein, it is demonstrated that said result cannot be generalized to arbitrary CFLs, leading to dedicated machinery for both cases.
Cite as

Corentin Barloy, Michaël Cadilhac, and Kyle Ockerlund. Shuffles of Context-Free Languages Along Regular Trajectories. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 163:1-163:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{barloy_et_al:LIPIcs.ICALP.2026.163,
  author =	{Barloy, Corentin and Cadilhac, Micha\"{e}l and Ockerlund, Kyle},
  title =	{{Shuffles of Context-Free Languages Along Regular Trajectories}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{163:1--163:17},
  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.2026.163},
  URN =		{urn:nbn:de:0030-drops-265513},
  doi =		{10.4230/LIPIcs.ICALP.2026.163},
  annote =	{Keywords: Context-free languages, shuffles, concurrency, non-regularity}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2026.167
Population Protocols over Ordered Agents

Authors: Michael Blondin, Michaël Cadilhac, Benjamin Courchesne, Lucie Guillou, Corto Mascle, and Isa Vialard

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

Abstract
Population protocols are a distributed computation model in which a collection of anonymous, finite-state agents interact in randomly chosen pairs and update their states according to a fixed transition function. The computation is defined by the eventual stabilization of the population to a consensus that represents the output. In practice, it is natural to allow each agent to carry a unique identifier and compare it with that of another agent before interacting. We model this extension by having agents be totally ordered and interactions between two agents to be fireable only if their pair of identifiers falls in some condition set. For instance, PP[<] allows for two agents to interact only if the first one appears before the second one. We study population protocols over ordered agents PP[𝒩] where 𝒩 is a set of predicates available to restrict transition firing. We also study IO-PP[𝒩], the immediate observation fragment of PP[𝒩] where only one agent changes state per interaction. Our main result is that IO-PP[<] recognizes exactly the unambiguous star-free languages, which admits many other characterizations, such as two-variable first-order logic or two-way deterministic partially-ordered automata. We also provide a logic and an automaton model that fits in PP[<]. We further show that if the successor predicate appears in a set 𝒩 of NSPACE(n)-computable predicates, then IO-PP[𝒩] = PP[𝒩] = NSPACE(n). Finally, we investigate the problem of deciding whether a given population protocol always stabilizes to a consensus. While this problem is decidable for unordered population protocols, we show that this is undecidable already for PP[<] and IO-PP[+1], but conditionally decidable for IO-PP[<].
Cite as

Michael Blondin, Michaël Cadilhac, Benjamin Courchesne, Lucie Guillou, Corto Mascle, and Isa Vialard. Population Protocols over Ordered Agents. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 167:1-167:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{blondin_et_al:LIPIcs.ICALP.2026.167,
  author =	{Blondin, Michael and Cadilhac, Micha\"{e}l and Courchesne, Benjamin and Guillou, Lucie and Mascle, Corto and Vialard, Isa},
  title =	{{Population Protocols over Ordered Agents}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{167:1--167:20},
  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.2026.167},
  URN =		{urn:nbn:de:0030-drops-265557},
  doi =		{10.4230/LIPIcs.ICALP.2026.167},
  annote =	{Keywords: Population protocols, First-order logic, Partially-ordered automata, Unambiguous star-free languages}
}
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.MFCS.2023.30
Parikh One-Counter Automata

Authors: Michaël Cadilhac, Arka Ghosh, Guillermo A. Pérez, and Ritam Raha

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
Counting abilities in finite automata are traditionally provided by two orthogonal extensions: adding a single counter that can be tested for zeroness at any point, or adding ℤ-valued counters that are tested for equality only at the end of runs. In this paper, finite automata extended with both types of counters are introduced. They are called Parikh One-Counter Automata (POCA): the "Parikh" part referring to the evaluation of counters at the end of runs, and the "One-Counter" part to the single counter that can be tested during runs. Their expressiveness, in the deterministic and nondeterministic variants, is investigated; it is shown in particular that there are deterministic POCA languages that cannot be expressed without nondeterminism in the original models. The natural decision problems are also studied; strikingly, most of them are no harder than in the original models. A parametric version of nonemptiness is also considered.
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Michaël Cadilhac, Arka Ghosh, Guillermo A. Pérez, and Ritam Raha. Parikh One-Counter Automata. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 30:1-30:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{cadilhac_et_al:LIPIcs.MFCS.2023.30,
  author =	{Cadilhac, Micha\"{e}l and Ghosh, Arka and P\'{e}rez, Guillermo A. and Raha, Ritam},
  title =	{{Parikh One-Counter Automata}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{30:1--30:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.30},
  URN =		{urn:nbn:de:0030-drops-185645},
  doi =		{10.4230/LIPIcs.MFCS.2023.30},
  annote =	{Keywords: Parikh automata, Context-free languages, One-counter automata}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2020.116
Rational Subsets of Baumslag-Solitar Groups

Authors: Michaël Cadilhac, Dmitry Chistikov, and Georg Zetzsche

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

Abstract
We consider the rational subset membership problem for Baumslag-Solitar groups. These groups form a prominent class in the area of algorithmic group theory, and they were recently identified as an obstacle for understanding the rational subsets of GL(2,ℚ). We show that rational subset membership for Baumslag-Solitar groups BS(1,q) with q ≥ 2 is decidable and PSPACE-complete. To this end, we introduce a word representation of the elements of BS(1,q): their pointed expansion (PE), an annotated q-ary expansion. Seeing subsets of BS(1,q) as word languages, this leads to a natural notion of PE-regular subsets of BS(1,q): these are the subsets of BS(1,q) whose sets of PE are regular languages. Our proof shows that every rational subset of BS(1,q) is PE-regular. Since the class of PE-regular subsets of BS(1,q) is well-equipped with closure properties, we obtain further applications of these results. Our results imply that (i) emptiness of Boolean combinations of rational subsets is decidable, (ii) membership to each fixed rational subset of BS(1,q) is decidable in logarithmic space, and (iii) it is decidable whether a given rational subset is recognizable. In particular, it is decidable whether a given finitely generated subgroup of BS(1,q) has finite index.
Cite as

Michaël Cadilhac, Dmitry Chistikov, and Georg Zetzsche. Rational Subsets of Baumslag-Solitar Groups. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 116:1-116:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{cadilhac_et_al:LIPIcs.ICALP.2020.116,
  author =	{Cadilhac, Micha\"{e}l and Chistikov, Dmitry and Zetzsche, Georg},
  title =	{{Rational Subsets of Baumslag-Solitar Groups}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{116:1--116:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.116},
  URN =		{urn:nbn:de:0030-drops-125238},
  doi =		{10.4230/LIPIcs.ICALP.2020.116},
  annote =	{Keywords: Rational subsets, Baumslag-Solitar groups, decidability, regular languages, pointed expansion}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2020.117
On Polynomial Recursive Sequences

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

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

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

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

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@InProceedings{cadilhac_et_al:LIPIcs.ICALP.2020.117,
  author =	{Cadilhac, Micha\"{e}l and Mazowiecki, Filip and Paperman, Charles and Pilipczuk, Micha{\l} and S\'{e}nizergues, G\'{e}raud},
  title =	{{On Polynomial Recursive Sequences}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{117:1--117:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.117},
  URN =		{urn:nbn:de:0030-drops-125240},
  doi =		{10.4230/LIPIcs.ICALP.2020.117},
  annote =	{Keywords: recursive sequences, expressive power, weighted automata, higher-order pushdown automata}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.115
Continuity and Rational Functions

Authors: Michaël Cadilhac, Olivier Carton, and Charles Paperman

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract
A word-to-word function is continuous for a class of languages V if its inverse maps V languages to V. This notion provides a basis for an algebraic study of transducers, and was integral to the characterization of the sequential transducers computable in some circuit complexity classes. Here, we report on the decidability of continuity for functional transducers and some standard classes of regular languages. Previous algebraic studies of transducers have focused on the structure of the underlying input automaton, disregarding the output. We propose a comparison of the two algebraic approaches through two questions: When are the automaton structure and the continuity properties related, and when does continuity propagate to superclasses?
Cite as

Michaël Cadilhac, Olivier Carton, and Charles Paperman. Continuity and Rational Functions. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 115:1-115:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{cadilhac_et_al:LIPIcs.ICALP.2017.115,
  author =	{Cadilhac, Micha\"{e}l and Carton, Olivier and Paperman, Charles},
  title =	{{Continuity and Rational Functions}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{115:1--115:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.115},
  URN =		{urn:nbn:de:0030-drops-74583},
  doi =		{10.4230/LIPIcs.ICALP.2017.115},
  annote =	{Keywords: Transducers, rational functions, language varieties, continuity}
}
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