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Documents authored by Barloy, Corentin

Document
DOI: 10.4230/LIPIcs.MFCS.2025.8
Dynamic Membership for Regular Tree Languages

Authors: Antoine Amarilli, Corentin Barloy, Louis Jachiet, and Charles Paperman

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

Abstract
We study the dynamic membership problem for regular tree languages under relabeling updates: we fix an alphabet Σ and a regular tree language L over Σ (expressed, e.g., as a tree automaton), we are given a tree T with labels in Σ, and we must maintain the information of whether the tree T belongs to L while handling relabeling updates that change the labels of individual nodes in T. Our first contribution is to show that this problem admits an O(log n / log log n) algorithm for any fixed regular tree language, improving over known O(log n) algorithms. This generalizes the known O(log n / log log n) upper bound over words, and it matches the lower bound of Ω(log n / log log n) from dynamic membership to some word languages and from the existential marked ancestor problem. Our second contribution is to introduce a class of regular languages, dubbed almost-commutative tree languages, and show that dynamic membership to such languages under relabeling updates can be decided in constant time per update. Almost-commutative languages generalize both commutative languages and finite languages: they are the analogue for trees of the ZG languages enjoying constant-time dynamic membership over words. Our main technical contribution is to show that this class is conditionally optimal when we assume that the alphabet features a neutral letter, i.e., a letter that has no effect on membership to the language. More precisely, we show that any regular tree language with a neutral letter which is not almost-commutative cannot be maintained in constant time under the assumption that the prefix-U1 problem from [Antoine Amarilli et al., 2021] also does not admit a constant-time algorithm.
Cite as

Antoine Amarilli, Corentin Barloy, Louis Jachiet, and Charles Paperman. Dynamic Membership for Regular Tree Languages. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{amarilli_et_al:LIPIcs.MFCS.2025.8,
  author =	{Amarilli, Antoine and Barloy, Corentin and Jachiet, Louis and Paperman, Charles},
  title =	{{Dynamic Membership for Regular Tree Languages}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{8:1--8:18},
  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.2025.8},
  URN =		{urn:nbn:de:0030-drops-241155},
  doi =		{10.4230/LIPIcs.MFCS.2025.8},
  annote =	{Keywords: automaton, dynamic membership, incremental maintenance, forest algebra}
}
Document
DOI: 10.4230/LIPIcs.STACS.2021.8
Bidimensional Linear Recursive Sequences and Universality of Unambiguous Register Automata

Authors: Corentin Barloy and Lorenzo Clemente

Published in: LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)

Abstract
We study the universality and inclusion problems for register automata over equality data (A, =). We show that the universality L(B) = (Σ × A)^* and inclusion problems L(A) ⊆ L(B) B can be solved with 2-EXPTIME complexity when both automata are without guessing and B is unambiguous, improving on the currently best-known 2-EXPSPACE upper bound by Mottet and Quaas. When the number of registers of both automata is fixed, we obtain a lower EXPTIME complexity, also improving the EXPSPACE upper bound from Mottet and Quaas for fixed number of registers. We reduce inclusion to universality, and then we reduce universality to the problem of counting the number of orbits of runs of the automaton. We show that the orbit-counting function satisfies a system of bidimensional linear recursive equations with polynomial coefficients (linrec), which generalises analogous recurrences for the Stirling numbers of the second kind, and then we show that universality reduces to the zeroness problem for linrec sequences. While such a counting approach is classical and has successfully been applied to unambiguous finite automata and grammars over finite alphabets, its application to register automata over infinite alphabets is novel. We provide two algorithms to decide the zeroness problem for bidimensional linear recursive sequences arising from orbit-counting functions. Both algorithms rely on techniques from linear non-commutative algebra. The first algorithm performs variable elimination and has elementary complexity. The second algorithm is a refined version of the first one and it relies on the computation of the Hermite normal form of matrices over a skew polynomial field. The second algorithm yields an EXPTIME decision procedure for the zeroness problem of linrec sequences, which in turn yields the claimed bounds for the universality and inclusion problems of register automata.
Cite as

Corentin Barloy and Lorenzo Clemente. Bidimensional Linear Recursive Sequences and Universality of Unambiguous Register Automata. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 8:1-8:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{barloy_et_al:LIPIcs.STACS.2021.8,
  author =	{Barloy, Corentin and Clemente, Lorenzo},
  title =	{{Bidimensional Linear Recursive Sequences and Universality of Unambiguous Register Automata}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{8:1--8:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.8},
  URN =		{urn:nbn:de:0030-drops-136533},
  doi =		{10.4230/LIPIcs.STACS.2021.8},
  annote =	{Keywords: unambiguous register automata, universality and inclusion problems, multi-dimensional linear recurrence sequences}
}
Document
DOI: 10.4230/LIPIcs.CSL.2020.9
A Robust Class of Linear Recurrence Sequences

Authors: Corentin Barloy, Nathanaël Fijalkow, Nathan Lhote, and Filip Mazowiecki

Published in: LIPIcs, Volume 152, 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)

Abstract
We introduce a subclass of linear recurrence sequences which we call poly-rational sequences because they are denoted by rational expressions closed under sum and product. We show that this class is robust by giving several characterisations: polynomially ambiguous weighted automata, copyless cost-register automata, rational formal series, and linear recurrence sequences whose eigenvalues are roots of rational numbers.
Cite as

Corentin Barloy, Nathanaël Fijalkow, Nathan Lhote, and Filip Mazowiecki. A Robust Class of Linear Recurrence Sequences. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{barloy_et_al:LIPIcs.CSL.2020.9,
  author =	{Barloy, Corentin and Fijalkow, Nathana\"{e}l and Lhote, Nathan and Mazowiecki, Filip},
  title =	{{A Robust Class of Linear Recurrence Sequences}},
  booktitle =	{28th EACSL Annual Conference on Computer Science Logic (CSL 2020)},
  pages =	{9:1--9:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-132-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{152},
  editor =	{Fern\'{a}ndez, Maribel 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.CSL.2020.9},
  URN =		{urn:nbn:de:0030-drops-116521},
  doi =		{10.4230/LIPIcs.CSL.2020.9},
  annote =	{Keywords: linear recurrence sequences, weighted automata, cost-register automata}
}
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