5 Search Results for "Lemay, Aurélien"

Document
DOI: 10.4230/LIPIcs.ICDT.2025.4
Learning Aggregate Queries Defined by First-Order Logic with Counting

Authors: Steffen van Bergerem and Nicole Schweikardt

Published in: LIPIcs, Volume 328, 28th International Conference on Database Theory (ICDT 2025)

Abstract
In the logical framework introduced by Grohe and Turán (TOCS 2004) for Boolean classification problems, the instances to classify are tuples from a logical structure, and Boolean classifiers are described by parametric models based on logical formulas. This is a specific scenario for supervised passive learning, where classifiers should be learned based on labelled examples. Existing results in this scenario focus on Boolean classification. This paper presents learnability results beyond Boolean classification. We focus on multiclass classification problems where the task is to assign input tuples to arbitrary integers. To represent such integer-valued classifiers, we use aggregate queries specified by an extension of first-order logic with counting terms called FOC₁. Our main result shows the following: given a database of polylogarithmic degree, within quasi-linear time, we can build an index structure that makes it possible to learn FOC₁-definable integer-valued classifiers in time polylogarithmic in the size of the database and polynomial in the number of training examples.
Cite as

Steffen van Bergerem and Nicole Schweikardt. Learning Aggregate Queries Defined by First-Order Logic with Counting. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{vanbergerem_et_al:LIPIcs.ICDT.2025.4,
  author =	{van Bergerem, Steffen and Schweikardt, Nicole},
  title =	{{Learning Aggregate Queries Defined by First-Order Logic with Counting}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{4:1--4:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.4},
  URN =		{urn:nbn:de:0030-drops-229457},
  doi =		{10.4230/LIPIcs.ICDT.2025.4},
  annote =	{Keywords: Supervised learning, multiclass classification problems, counting logic}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.68
Slightly Non-Linear Higher-Order Tree Transducers

Authors: Lê Thành Dũng (Tito) Nguyễn and Gabriele Vanoni

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
We investigate the tree-to-tree functions computed by "affine λ-transducers": tree automata whose memory consists of an affine λ-term instead of a finite state. They can be seen as variations on Gallot, Lemay and Salvati’s Linear High-Order Deterministic Tree Transducers. When the memory is almost purely affine (à la Kanazawa), we show that these machines can be translated to tree-walking transducers (and with a purely affine memory, we get a reversible tree-walking transducer). This leads to a proof of an inexpressivity conjecture of Nguyễn and Pradic on "implicit automata" in an affine λ-calculus. We also prove that a more powerful variant, extended with preprocessing by an MSO relabeling and allowing a limited amount of non-linearity, is equivalent in expressive power to Engelfriet, Hoogeboom and Samwel’s invisible pebble tree transducers. The key technical tool in our proofs is the Interaction Abstract Machine (IAM), an operational avatar of Girard’s geometry of interaction, a semantics of linear logic. We work with ad-hoc specializations to λ-terms of low exponential depth of a tree-generating version of the IAM.
Cite as

Lê Thành Dũng (Tito) Nguyễn and Gabriele Vanoni. Slightly Non-Linear Higher-Order Tree Transducers. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 68:1-68:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{nguyen_et_al:LIPIcs.STACS.2025.68,
  author =	{Nguy\~{ê}n, L\^{e} Th\`{a}nh D\~{u}ng (Tito) and Vanoni, Gabriele},
  title =	{{Slightly Non-Linear Higher-Order Tree Transducers}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{68:1--68:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.68},
  URN =		{urn:nbn:de:0030-drops-228934},
  doi =		{10.4230/LIPIcs.STACS.2025.68},
  annote =	{Keywords: Almost affine lambda-calculus, geometry of interaction, reversibility, tree transducers, tree-walking automata}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.8
The Parameterized Complexity of Learning Monadic Second-Order Logic

Authors: Steffen van Bergerem, Martin Grohe, and Nina Runde

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

Abstract
Within the model-theoretic framework for supervised learning introduced by Grohe and Turán (TOCS 2004), we study the parameterized complexity of learning concepts definable in monadic second-order logic (MSO). We show that the problem of learning an MSO-definable concept from a training sequence of labeled examples is fixed-parameter tractable on graphs of bounded clique-width, and that it is hard for the parameterized complexity class para-NP on general graphs. It turns out that an important distinction to be made is between 1-dimensional and higher-dimensional concepts, where the instances of a k-dimensional concept are k-tuples of vertices of a graph. For the higher-dimensional case, we give a learning algorithm that is fixed-parameter tractable in the size of the graph, but not in the size of the training sequence, and we give a hardness result showing that this is optimal. By comparison, in the 1-dimensional case, we obtain an algorithm that is fixed-parameter tractable in both.
Cite as

Steffen van Bergerem, Martin Grohe, and Nina Runde. The Parameterized Complexity of Learning Monadic Second-Order Logic. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{vanbergerem_et_al:LIPIcs.CSL.2025.8,
  author =	{van Bergerem, Steffen and Grohe, Martin and Runde, Nina},
  title =	{{The Parameterized Complexity of Learning Monadic Second-Order Logic}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{8:1--8:19},
  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.2025.8},
  URN =		{urn:nbn:de:0030-drops-227651},
  doi =		{10.4230/LIPIcs.CSL.2025.8},
  annote =	{Keywords: monadic second-order definable concept learning, agnostic probably approximately correct learning, parameterized complexity, clique-width, fixed-parameter tractable, Boolean classification, supervised learning, monadic second-order logic}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2022.14
Inference of Shape Graphs for Graph Databases

Authors: Benoît Groz, Aurélien Lemay, Sławek Staworko, and Piotr Wieczorek

Published in: LIPIcs, Volume 220, 25th International Conference on Database Theory (ICDT 2022)

Abstract
We investigate the problem of constructing a shape graph that describes the structure of a given graph database. We employ the framework of grammatical inference, where the objective is to find an inference algorithm that is both sound, i.e., always producing a schema that validates the input graph, and complete, i.e., able to produce any schema, within a given class of schemas, provided that a sufficiently informative input graph is presented. We identify a number of fundamental limitations that preclude feasible inference. We present inference algorithms based on natural approaches that allow to infer schemas that we argue to be of practical importance.
Cite as

Benoît Groz, Aurélien Lemay, Sławek Staworko, and Piotr Wieczorek. Inference of Shape Graphs for Graph Databases. In 25th International Conference on Database Theory (ICDT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 220, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{groz_et_al:LIPIcs.ICDT.2022.14,
  author =	{Groz, Beno\^{i}t and Lemay, Aur\'{e}lien and Staworko, S{\l}awek and Wieczorek, Piotr},
  title =	{{Inference of Shape Graphs for Graph Databases}},
  booktitle =	{25th International Conference on Database Theory (ICDT 2022)},
  pages =	{14:1--14:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-223-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{220},
  editor =	{Olteanu, Dan and Vortmeier, Nils},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2022.14},
  URN =		{urn:nbn:de:0030-drops-158889},
  doi =		{10.4230/LIPIcs.ICDT.2022.14},
  annote =	{Keywords: RDF, Schema, Inference, Learning, Fitting, Minimality, Containment}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.38
Linear High-Order Deterministic Tree Transducers with Regular Look-Ahead

Authors: Paul D. Gallot, Aurélien Lemay, and Sylvain Salvati

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
We introduce the notion of high-order deterministic top-down tree transducers (HODT) whose outputs correspond to single-typed lambda-calculus formulas. These transducers are natural generalizations of known models of top-tree transducers such as: Deterministic Top-Down Tree Transducers, Macro Tree Transducers, Streaming Tree Transducers... We focus on the linear restriction of high order tree transducers with look-ahead (HODTR_lin), and prove this corresponds to tree to tree functional transformations defined by Monadic Second Order (MSO) logic. We give a specialized procedure for the composition of those transducers that uses a flow analysis based on coherence spaces and allows us to preserve the linearity of transducers. This procedure has a better complexity than classical algorithms for composition of other equivalent tree transducers, but raises the order of transducers. However, we also indicate that the order of a HODTR_lin can always be bounded by 3, and give a procedure that reduces the order of a HODTR_lin to 3. As those resulting HODTR_lin can then be transformed into other equivalent models, this gives an important insight on composition algorithm for other classes of transducers. Finally, we prove that those results partially translate to the case of almost linear HODTR: the class corresponds to the class of tree transformations performed by MSO with unfolding (not closed by composition), and provide a mechanism to reduce the order to 3 in this case.
Cite as

Paul D. Gallot, Aurélien Lemay, and Sylvain Salvati. Linear High-Order Deterministic Tree Transducers with Regular Look-Ahead. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 38:1-38:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{gallot_et_al:LIPIcs.MFCS.2020.38,
  author =	{Gallot, Paul D. and Lemay, Aur\'{e}lien and Salvati, Sylvain},
  title =	{{Linear High-Order Deterministic Tree Transducers with Regular Look-Ahead}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{38:1--38:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.38},
  URN =		{urn:nbn:de:0030-drops-127050},
  doi =		{10.4230/LIPIcs.MFCS.2020.38},
  annote =	{Keywords: Transducers, \lambda-calculus, Trees}
}
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