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authoraristote <quentin.aristote@irif.fr>2025-07-26 23:38:08 +0200
committeraristote <quentin.aristote@irif.fr>2025-07-26 23:38:08 +0200
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+---
+references:
+- id: aristoteActiveLearningDeterministic2024a
+ abstract: >-
+ We study monoidal transducers, transition systems arising as deterministic
+ automata whose transitions also produce outputs in an arbitrary monoid, for
+ instance allowing outputs to commute or to cancel out. We use the
+ categorical framework for minimization and learning of Colcombet, Petrişan
+ and Stabile to recover the notion of minimal transducer recognizing a
+ language, and give necessary and sufficient conditions on the output monoid
+ for this minimal transducer to exist and be unique (up to isomorphism). The
+ categorical framework then provides an abstract algorithm for learning it
+ using membership and equivalence queries, and we discuss practical aspects
+ of this algorithm’s implementation.
+ author:
+ - family: Aristote
+ given: Quentin
+ citation-key: aristoteActiveLearningDeterministic2024a
+ event-place: Naples, Italy
+ event-title: 32nd EACSL Annual Conference on Computer Science Logic 2024 (CSL 2024)
+ genre: conference
+ issued:
+ - year: 2024
+ month: 2
+ day: 22
+ language: en
+ note: >-
+ slides:
+ https://gitlab.math.univ-paris-diderot.fr/-/project/840/uploads/441b176a634e9ed8b569d75dc18bf98a/monoidal-transducer-learning.pdf
+ publisher-place: Naples, Italy
+ title: >-
+ Active Learning of Deterministic Transducers with Outputs in Arbitrary
+ Monoids
+ type: speech
+ URL: https://www.irif.fr/seminaires/automates/index
+
+- id: aristoteActiveLearningDeterministic2024b
+ abstract: >-
+ We study monoidal transducers, transition systems arising as deterministic
+ automata whose transitions also produce outputs in an arbitrary monoid, for
+ instance allowing outputs to commute or to cancel out. In a first part I'll
+ explain how Vilar's algorithm for the active learning à la Angluin of
+ (normal) transducers generalize to monoidal transducers. In a second part
+ I'll then discuss how this is an instance of the categorical framework for
+ minimization and learning of Colcombet, Petrişan and Stabile: the active
+ learning algorithm was obtained by instantiating monoidal transducers in
+ this framework.
+ author:
+ - family: Aristote
+ given: Quentin
+ citation-key: aristoteActiveLearningDeterministic2024b
+ event-place: Paris, France
+ event-title: Séminaire Automates (IRIF)
+ genre: seminar
+ issued:
+ - year: 2024
+ month: 3
+ day: 22
+ language: en
+ note: >-
+ slides:
+ https://gitlab.math.univ-paris-diderot.fr/-/project/840/uploads/46406ee1029eeaa311f952e661cc742c/monoidal-transducer-learning.pdf
+ publisher-place: Paris, France
+ title: >-
+ Active Learning of Deterministic Transducers with Outputs in Arbitrary
+ Monoids
+ type: speech
+ URL: https://www.irif.fr/seminaires/automates/index
+
+- id: aristoteActiveLearningDeterministic2024c
+ abstract: >-
+ We study monoidal transducers, transition systems arising as deterministic
+ automata whose transitions also produce outputs in an arbitrary monoid, for
+ instance allowing outputs to commute or to cancel out. In a first part I'll
+ explain how Vilar's algorithm for the active learning à la Angluin of
+ (normal) transducers generalize to monoidal transducers. In a second part
+ I'll then discuss how this is an instance of the categorical framework for
+ minimization and learning of Colcombet, Petrişan and Stabile: the active
+ learning algorithm was obtained by instantiating monoidal transducers in
+ this framework.
+ author:
+ - family: Aristote
+ given: Quentin
+ citation-key: aristoteActiveLearningDeterministic2024c
+ event-place: Oxford, United Kingdom
+ event-title: Verification seminar
+ genre: seminar
+ issued:
+ - year: 2024
+ month: 6
+ day: 17
+ language: en
+ note: >-
+ slides:
+ https://gitlab.math.univ-paris-diderot.fr/-/project/840/uploads/46406ee1029eeaa311f952e661cc742c/monoidal-transducer-learning.pdf
+ publisher-place: Oxford, United Kingdom
+ title: >-
+ Active Learning of Deterministic Transducers with Outputs in Arbitrary
+ Monoids
+ type: speech
+ URL: https://www.cs.ox.ac.uk/research/verification/
+
+- id: aristoteActiveLearningUpwardclosed2025a
+ 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.
+ author:
+ - family: Aristote
+ given: Quentin
+ citation-key: aristoteActiveLearningUpwardclosed2025a
+ event-place: Glasgow, Scotland$
+ event-title: 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)
+ genre: conference
+ issued:
+ - year: 2025
+ month: 6
+ day: 17
+ language: en
+ note: >-
+ slides:
+ https://coalg.org/calco-mfps-2025/slides/2-Tuesday/4-Session3/1-QuentinAristote.pdf
+ publisher-place: Glasgow, Scotland$
+ title: Active learning of upward-closed sets of words
+ type: speech
+ URL: https://coalg.org/calco-mfps-2025/calco/
+
+- id: aristoteAutomataWeightedCommutative2023
+ author:
+ - family: Aristote
+ given: Quentin
+ citation-key: aristoteAutomataWeightedCommutative2023
+ event-place: Paris, France
+ event-title: ASV day (IRIF)
+ genre: seminar
+ issued:
+ - year: 2023
+ month: 12
+ day: 6
+ language: en
+ note: >-
+ slides:
+ https://gitlab.math.univ-paris-diderot.fr/-/project/996/uploads/48a134fb160ea880ea4676adbf1dc637/dedekind-weighted-automata.pdf
+ publisher-place: Paris, France
+ title: >-
+ Automata weighted over commutative rings: notions of minimality and the case
+ of Dedekind domains
+ type: speech
+ URL: https://www.irif.fr/poles/asv/journee_pole_2023
+
+- id: aristoteLearningWeightedAutomata2025a
+ abstract: >-
+ We study automata weighted over number rings, that is, rings of integers in
+ an algebraic number field.
+
+
+ We show that number rings are what we call "almost strong Fatou": if an
+ n-state automaton weighted in a number field recognizes an integer-valued
+ series, then it admits an equivalent n+1-state automaton weighted in the
+ corresponding ring of integers.
+
+
+ We give a polynomial-time algorithm for computing such an n+1-state
+ automaton, and show that removing any more states is at least as hard as
+ solving the principal ideal problem, for which the best currently known
+ algorithm is in quantum polynomial time.
+
+
+ Finally, we will see how this procedure can be used to reduce active
+ learning problems in number rings to active learning problems in fields. If
+ time allows, I will also give a brief explanation of how this generalizes to
+ a generic reduction procedure between active learning problems for automata
+ valued in different categories.
+ author:
+ - family: Aristote
+ given: Quentin
+ citation-key: aristoteLearningWeightedAutomata2025a
+ event-place: Marseille, France
+ event-title: MoVe seminar (LiS)
+ genre: seminar
+ issued:
+ - year: 2025
+ month: 3
+ day: 28
+ language: en
+ note: >-
+ slides:
+ https://gitlab.math.univ-paris-diderot.fr/-/project/996/uploads/8b14ed9a7383f9776fc69aa03003890a/dedekind-weighted-automata.pdf
+ publisher-place: Marseille, France
+ title: Learning Weighted Automata over Number Rings, Concretely (and Categorically)
+ type: speech
+ URL: https://move.lis-lab.fr/seminars
+
+- id: aristoteLearningWeightedAutomata2025b
+ abstract: >-
+ We develop a generic reduction procedure for active learning problems. Our
+ approach is inspired by a recent polynomial-time reduction of the exact
+ learning problem for weighted automata over integers to that for weighted
+ automata over rationals (Buna-Marginean et al. 2024). Our procedure improves
+ the efficiency of a category-theoretic automata learning algorithm, and
+ poses new questions about the complexity of its implementation when
+ instantiated to concrete categories.
+
+
+ As our second main contribution, we address these complexity aspects in the
+ concrete setting of learning weighted automata over number rings, that is,
+ rings of integers in an algebraic number field. Assuming a full
+ representation of a number ring OK, we obtain an exact learning algorithm of
+ OK-weighted automata that runs in polynomial time in the size of the target
+ automaton, the logarithm of the length of the longest counterexample, the
+ degree of the number field, and the logarithm of its discriminant. Our
+ algorithm produces an automaton that has at most one more state than the
+ minimal one, and we prove that doing better requires solving the principal
+ ideal problem, for which the best currently known algorithm is in quantum
+ polynomial time.
+ author:
+ - family: Aristote
+ given: Quentin
+ citation-key: aristoteLearningWeightedAutomata2025b
+ event-place: Wadern, Germany
+ event-title: Dagstuhl Seminar 25141 Categories for Automata and Language Theory
+ genre: conference
+ issued:
+ - year: 2025
+ month: 3
+ day: 31
+ language: en
+ note: 'slides: https://materials.dagstuhl.de/index.php?semnr=25141&fileId=17258'
+ publisher-place: Wadern, Germany
+ title: Learning Weighted Automata over Number Rings, (Concretely and) Categorically
+ type: speech
+ URL: https://www.dagstuhl.de/25141
+
+- id: aristoteLearningWeightedAutomata2025c
+ abstract: >-
+ We develop a generic reduction procedure for active learning problems. Our
+ approach is inspired by a recent polynomial-time reduction of the exact
+ learning problem for weighted automata over integers to that for weighted
+ automata over rationals (Buna-Marginean et al. 2024). Our procedure improves
+ the efficiency of a category-theoretic automata learning algorithm, and
+ poses new questions about the complexity of its implementation when
+ instantiated to concrete categories.
+
+
+ As our second main contribution, we address these complexity aspects in the
+ concrete setting of learning weighted automata over number rings, that is,
+ rings of integers in an algebraic number field. Assuming a full
+ representation of a number ring OK, we obtain an exact learning algorithm of
+ OK-weighted automata that runs in polynomial time in the size of the target
+ automaton, the logarithm of the length of the longest counterexample, the
+ degree of the number field, and the logarithm of its discriminant. Our
+ algorithm produces an automaton that has at most one more state than the
+ minimal one, and we prove that doing better requires solving the principal
+ ideal problem, for which the best currently known algorithm is in quantum
+ polynomial time.
+ author:
+ - family: Aristote
+ given: Quentin
+ citation-key: aristoteLearningWeightedAutomata2025c
+ event-place: Singapore, Singapore
+ event-title: Fortieth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2025)
+ genre: conference
+ issued:
+ - year: 2025
+ month: 6
+ day: 24
+ language: en
+ note: >-
+ slides:
+ https://gitlab.math.univ-paris-diderot.fr/-/project/996/uploads/13561d884f911e1e27f5df625892bfb1/dedekind-weighted-automata.pdf
+ publisher-place: Singapore, Singapore
+ title: Learning Weighted Automata over Number Rings, Concretely and Categorically
+ type: speech
+ URL: https://lics.siglog.org/lics25/
+
+- id: aristoteMonotoneWeakDistributive2024a
+ abstract: >-
+ Noticing the similarity between the monotone weak distributive laws
+ combining two layers of nondeterminisms in sets and in compact Hausdorff
+ spaces, we study whether the latter law can be obtained automatically as a
+ weak lifting of the former. This holds partially, but does not generalize to
+ other categories of algebras: we then characterize when exactly monotone
+ weak distributive laws over powerset monads in categories of algebras exist,
+ exhibiting a law combining probabilities and non-determinism in compact
+ Hausdorff spaces and showing on the other hand that such laws do not exist
+ in a lot of other cases.
+ author:
+ - family: Aristote
+ given: Quentin
+ citation-key: aristoteMonotoneWeakDistributive2024a
+ event-place: Leiden, The Netherlands
+ event-title: 109th Peripatetic Seminar on Sheaves and Logic (PSSL 109)
+ genre: conference
+ issued:
+ - year: 2024
+ month: 11
+ day: 15
+ language: en
+ note: >-
+ slides:
+ https://dutchcats.github.io/PSSL-2024/slides_PSSL24/Aristote-PSSL109.pdf
+ publisher-place: Leiden, The Netherlands
+ title: >-
+ Monotone weak distributive laws over the lifted powerset monad in categories
+ of algebras
+ type: speech
+ URL: https://dutchcats.github.io/PSSL-2024/
+
+- id: aristoteMonotoneWeakDistributive2025a
+ abstract: >-
+ In both the category of sets and the category of compact Hausdorff spaces,
+ there is a monotone weak distributive law that combines two layers of
+ non-determinism. Noticing the similarity between these two laws, we study
+ whether the latter can be obtained automatically as a weak lifting of the
+ former. This holds partially, but does not generalize to other categories of
+ algebras. We then characterize when exactly monotone weak distributive laws
+ over powerset monads in categories of algebras exist, on the one hand
+ exhibiting a law combining probabilities and non-determinism in compact
+ Hausdorff spaces and showing on the other hand that such laws do not exist
+ in a lot of other cases.
+ author:
+ - family: Aristote
+ given: Quentin
+ citation-key: aristoteMonotoneWeakDistributive2025a
+ event-place: Jena, Germany
+ event-title: >-
+ 42nd International Symposium on Theoretical Aspects of Computer Science
+ (STACS 2025)
+ genre: conference
+ issued:
+ - year: 2025
+ month: 3
+ day: 5
+ language: en
+ note: >-
+ slides:
+ https://stacs2025.gitlab.io/slides/monotone-weak-distributive-laws-over-the-lifted-powerset-monad-in-categories-of-algebras.pdf
+ publisher-place: Jena, Germany
+ title: >-
+ Monotone weak distributive laws over the lifted powerset monad in categories
+ of algebras
+ type: speech
+ URL: https://stacs2025.de/
+
+- id: aristoteMonotoneWeakDistributive2025b
+ abstract: >-
+ Within the study of the semantics of programming languages, computational
+ effects may be modelled with monads, and weak distributive laws between
+ monads are then a tool to combine two such effects.
+
+
+ In both the category of sets and the category of compact Hausdorff spaces,
+ there is a monotone weak distributive law that combines two layers of
+ non-determinism. Noticing the similarity between these two laws, we study
+ whether the latter can be obtained automatically as some sort of lifting of
+ the former.
+
+
+ More specifically, we show how a framework for constructing monotone weak
+ distributive laws in regular categories lifts to categories of algebras,
+ giving a full characterization for the existence of monotone weak
+ distributive laws therein. We then exhibit such a law, combining
+ probabilities and non-determinism, in compact Hausdorff spaces; but we also
+ show how such laws do not exist in a lot of other cases.
+ author:
+ - family: Aristote
+ given: Quentin
+ citation-key: aristoteMonotoneWeakDistributive2025b
+ event-place: Marseille, France
+ event-title: LSC Seminar (LiS)
+ genre: seminar
+ issued:
+ - year: 2025
+ month: 3
+ day: 27
+ language: en
+ note: >-
+ slides:
+ https://gitlab.math.univ-paris-diderot.fr/-/project/1062/uploads/02cd7ed45cdac419f5cf315fdde2200a/monotone-wdl-algebras.pdf
+ publisher-place: Marseille, France
+ title: >-
+ Monotone weak distributive laws over the lifted powerset monad in categories
+ of algebras
+ type: speech
+ URL: https://lsc.lis-lab.fr/lsc-seminar/
+
+- id: aristoteMonotoneWeakDistributive2025c
+ abstract: >-
+ When studying the semantics of programming languages, monads are a tool to
+ model computational effects. Given two monads modelling two effects, a
+ natural question is whether one can build a composed monad modelling the
+ combination of these two effects. There is a generic way to do this when
+ there exists a monotone weak distributive law between the two monads.
+
+
+ Monotone weak distributive laws are a recently-developed mathematical tool,
+ and the first part of the talk will focus on introducing them and giving
+ several examples. The second part of the talk will then focus on the main
+ result from [1], which gives a full characterization for the existence of
+ monotone weak distributive laws in certain categories of algebras.
+
+
+ [1] https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.10
+ author:
+ - family: Aristote
+ given: Quentin
+ citation-key: aristoteMonotoneWeakDistributive2025c
+ event-place: Palaiseau, France
+ event-title: Theoretical Cosynus Seminar (LIX)
+ genre: seminar
+ issued:
+ - year: 2025
+ month: 4
+ day: 8
+ language: en
+ publisher-place: Palaiseau, France
+ title: Monotone weak distributive laws in categories of algebras
+ type: speech
+ URL: https://www.lix.polytechnique.fr/proofs-algorithms/tcs/
+
+- id: aristoteMulticategoricalFrameworkMinimization2024
+ abstract: >-
+ Joint work with Daniela Petrişan. This paper provides a unifying
+ category-theoretic framework for minimization and learning algorithms for
+ bottom-up tree automata with effects. Our aim is two-fold: encompass
+ existing algorithms for various forms of tree automata – deterministic
+ bottom-up tree automata, residual finite tree automata, tree automata
+ weighted over a field – and instantiate the abstract framework in order to
+ obtain new results – tree automata weighted over prinicipal ideal domains
+ (PIDs).
+ author:
+ - family: Aristote
+ given: Quentin
+ citation-key: aristoteMulticategoricalFrameworkMinimization2024
+ event-place: Bordeaux, France
+ event-title: Highlights of Logic, Games and Automata (Highlights 2024)
+ genre: conference
+ issued:
+ - year: 2024
+ month: 9
+ day: 18
+ language: en
+ note: >-
+ slides:
+ https://gitlab.math.univ-paris-diderot.fr/-/project/1003/uploads/c415dcc8a1e22c5d91cb91cfd8d6d55f/minimal-tree-automata.pdf
+ publisher-place: Bordeaux, France
+ title: >-
+ Multicategorical framework for minimization and learning of bottom-up tree
+ automata with effects
+ type: speech
+ URL: https://highlights-conference.org/2024/
+
+- id: aristoteOpenPowerObjectsCategories2025
+ author:
+ - family: Aristote
+ given: Quentin
+ citation-key: aristoteOpenPowerObjectsCategories2025
+ event-place: Brno, Czech Republic
+ event-title: International Category Theory Conference (CT 2025)
+ genre: conference
+ issued:
+ - year: 2025
+ month: 7
+ day: 18
+ language: en
+ note: >-
+ slides:
+ https://gitlab.math.univ-paris-diderot.fr/-/project/1062/uploads/620105dfc6c8ec7fef78737368585a25/open-powerobjects-algebras.pdf
+
+ abstract:
+ https://conference.math.muni.cz/ct2025/data/uploads/abstracts/aristote.pdf
+ publisher-place: Brno, Czech Republic
+ title: Open Power-Objects in Categories of Algebras
+ type: speech
+ URL: https://conference.math.muni.cz/ct2025/
+
+- id: aristoteWeakDistributiveLaws2024
+ author:
+ - family: Aristote
+ given: Quentin
+ citation-key: aristoteWeakDistributiveLaws2024
+ event-place: Barcelona, Spain
+ event-title: Topology, Algebra, and Categories in Logic (TACL 2024)
+ genre: conference
+ issued:
+ - year: 2024
+ month: 7
+ day: 4
+ language: en
+ note: >-
+ slides:
+ https://gitlab.math.univ-paris-diderot.fr/-/project/1057/uploads/a2a13506a3034d6713fa0786adbc9ebf/wdl-powerspaces-scs.pdf
+
+ abstract:
+ https://iiia.csic.es/tacl2024/abstracts/conference/contributed/TACL_2024_paper_118.pdf
+ publisher-place: Barcelona, Spain
+ title: Weak distributive laws between powerspaces over stably compact spaces
+ type: speech
+ URL: https://iiia.csic.es/tacl2024/
+...