@unpublished{aristoteNumberRingsAre2025,
  author = {Aristote, Quentin},
  title = {Number Rings Are Almost Strong {Fatou}},
  date = {2025-09-29},
  address = {Marseille, France},
  url = {http://www.discmath.ulg.ac.be/CANT2025/},
  langid = {en},
  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
    procedure for computing such an n+1-state integer-weighted
    automaton, and show that deciding whether this automaton is minimal
    among all equivalent integer-weighted automata is as hard as PIP, a
    problem for which the best known algorithm is in quantum polynomial
    time. This procedure provides a reduction between learning problems
    for automata weighted in number rings and in fields, and we show
    that it is an instance of a more general, abstract reduction
    procedure between learning problems for automata valued in two
    categories related by well-behaved functors.}
}

@unpublished{aristoteNumberRingsAre2025,
  author = {Aristote, Quentin},
  title = {Number Rings Are Almost Strong {Fatou}},
  year = {2025},
  month = {sep},
  address = {Marseille, France},
  url = {http://www.discmath.ulg.ac.be/CANT2025/}
}

{"id":"aristoteNumberRingsAre2025","abstract":"We study automata weighted over number rings, that is, rings of integers in an algebraic number field.\n\nWe 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.\n\nWe give a polynomial time procedure for computing such an n+1-state integer-weighted automaton, and show that deciding whether this automaton is minimal among all equivalent integer-weighted automata is as hard as PIP, a problem for which the best known algorithm is in quantum polynomial time.\n\nThis procedure provides a reduction between learning problems for automata weighted in number rings and in fields, and we show that it is an instance of a more general, abstract reduction procedure between learning problems for automata valued in two categories related by well-behaved functors.","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteNumberRingsAre2025","event-place":"Marseille, France","event-title":"Combinatorics, Automata and Number Theory 2025","genre":"conference","issued":{"date-parts":[["2025",9,29]]},"language":"en","note":"slides: https://www.cirm-math.fr/RepOrga/3355/Slides/Aristote.pdfposter: https://gitlab.math.univ-paris-diderot.fr/-/project/996/uploads/6c9a3e6d87931780518a540aabb432de/removing-fractions.pdf","publisher-place":"Marseille, France","title":"Number rings are almost strong Fatou","type":"speech","URL":"http://www.discmath.ulg.ac.be/CANT2025/"}

@unpublished{aristoteLearningWeightedAutomata2025f,
  author = {Aristote, Quentin},
  title = {Learning Weighted Automata over Number Rings, Concretely (and
    Categorically)},
  date = {2025-09-02},
  address = {Saarbrücken, Germany},
  url = {https://highlights-conference.org/2025},
  langid = {en},
  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
    procedure for computing such an n+1-state integer-weighted
    automaton, and show that deciding whether this automaton is minimal
    among all equivalent integer-weighted automata is as hard as PIP, a
    problem for which the best known algorithm is in quantum polynomial
    time. This procedure provides a reduction between learning problems
    for automata weighted in number rings and in fields, and we show
    that it is an instance of a more general, abstract reduction
    procedure between learning problems for automata valued in two
    categories related by well-behaved functors.}
}

@unpublished{aristoteLearningWeightedAutomata2025f,
  author = {Aristote, Quentin},
  title = {Learning Weighted Automata over Number Rings, Concretely (and
    Categorically)},
  year = {2025},
  month = {sep},
  address = {Saarbrücken, Germany},
  url = {https://highlights-conference.org/2025}
}

{"id":"aristoteLearningWeightedAutomata2025f","abstract":"We study automata weighted over number rings, that is, rings of integers in an algebraic number field.\n\nWe 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.\n\nWe give a polynomial time procedure for computing such an n+1-state integer-weighted automaton, and show that deciding whether this automaton is minimal among all equivalent integer-weighted automata is as hard as PIP, a problem for which the best known algorithm is in quantum polynomial time.\n\nThis procedure provides a reduction between learning problems for automata weighted in number rings and in fields, and we show that it is an instance of a more general, abstract reduction procedure between learning problems for automata valued in two categories related by well-behaved functors.","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteLearningWeightedAutomata2025f","event-place":"Saarbrücken, Germany","event-title":"Highlights of Logic, Automata and Games 2025","genre":"conference","issued":{"date-parts":[["2025",9,2]]},"language":"en","note":"slides: https://gitlab.math.univ-paris-diderot.fr/-/project/996/uploads/30f2c03ecd247d85d4c36d823efceac8/numberrings-weighted-automata.pdf\nposter: https://gitlab.math.univ-paris-diderot.fr/-/project/996/uploads/6c9a3e6d87931780518a540aabb432de/removing-fractions.pdf","publisher-place":"Saarbrücken, Germany","title":"Learning weighted automata over number rings, concretely (and categorically)","type":"speech","URL":"https://highlights-conference.org/2025"}

@unpublished{aristoteOpenPowerObjectsCategories2025,
  author = {Aristote, Quentin},
  title = {Open {Power-Objects} in {Categories} of {Algebras}},
  date = {2025-07-18},
  address = {Brno, Czech Republic},
  url = {https://conference.math.muni.cz/ct2025/},
  langid = {en},
  abstract = {https://conference.math.muni.cz/ct2025/data/uploads/abstracts/aristote.pdf}
}

@unpublished{aristoteOpenPowerObjectsCategories2025,
  author = {Aristote, Quentin},
  title = {Open {Power-Objects} in {Categories} of {Algebras}},
  year = {2025},
  month = {jul},
  address = {Brno, Czech Republic},
  url = {https://conference.math.muni.cz/ct2025/}
}

{"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":{"date-parts":[["2025",7,18]]},"language":"en","note":"slides: https://gitlab.math.univ-paris-diderot.fr/-/project/1062/uploads/620105dfc6c8ec7fef78737368585a25/open-powerobjects-algebras.pdf\nabstract: 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/"}

@unpublished{aristoteLearningWeightedAutomata2025c,
  author = {Aristote, Quentin},
  title = {Learning Weighted Automata over Number Rings, Concretely and
    Categorically},
  date = {2025-06-24},
  address = {Singapore, Singapore},
  url = {https://lics.siglog.org/lics25/},
  langid = {en},
  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.}
}

@unpublished{aristoteLearningWeightedAutomata2025c,
  author = {Aristote, Quentin},
  title = {Learning Weighted Automata over Number Rings, Concretely and
    Categorically},
  year = {2025},
  month = {jun},
  address = {Singapore, Singapore},
  url = {https://lics.siglog.org/lics25/}
}

{"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.\n\nAs 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":{"date-parts":[["2025",6,24]]},"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/"}

@unpublished{aristoteActiveLearningUpwardclosed2025a,
  author = {Aristote, Quentin},
  title = {Active Learning of Upward-Closed Sets of Words},
  date = {2025-06-17},
  address = {Glasgow, Scotland},
  url = {https://coalg.org/calco-mfps-2025/calco/},
  langid = {en},
  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.}
}

@unpublished{aristoteActiveLearningUpwardclosed2025a,
  author = {Aristote, Quentin},
  title = {Active Learning of Upward-Closed Sets of Words},
  year = {2025},
  month = {jun},
  address = {Glasgow, Scotland},
  url = {https://coalg.org/calco-mfps-2025/calco/}
}

{"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.\n\nAlong 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":{"date-parts":[["2025",6,17]]},"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/"}

@unpublished{aristoteLearningWeightedAutomata2025e,
  author = {Aristote, Quentin},
  title = {Learning Weighted Automata over Number Rings, Concretely and
    Categorically},
  date = {2025-05-13},
  address = {Marne-la-Vallée, France},
  url = {https://www-igm.univ-mlv.fr/~marsault/daal2025/},
  langid = {en},
  abstract = {We study automata weighted over number rings, that is
    rings of integers in an algebraic number field. Assuming a full
    representation of a number ring O\_K, we obtain an exact learning
    algorithm of O\_K-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. More generally, 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), and improves the efficiency of a
    category-theoretic automata learning algorithm.}
}

@unpublished{aristoteLearningWeightedAutomata2025e,
  author = {Aristote, Quentin},
  title = {Learning Weighted Automata over Number Rings, Concretely and
    Categorically},
  year = {2025},
  month = {may},
  address = {Marne-la-Vallée, France},
  url = {https://www-igm.univ-mlv.fr/~marsault/daal2025/}
}

{"id":"aristoteLearningWeightedAutomata2025e","abstract":"We study automata weighted over number rings, that is rings of integers in an algebraic number field. Assuming a full representation of a number ring O_K, we obtain an exact learning algorithm of O_K-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.\n\nMore generally, 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), and improves the efficiency of a category-theoretic automata learning algorithm.","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteLearningWeightedAutomata2025e","event-place":"Marne-la-Vallée, France","event-title":"Annual Meeting ot the GT Data, Automata, Algebra & Logic (DAAL)","genre":"conference","issued":{"date-parts":[["2025",5,13]]},"language":"en","note":"slides: https://gitlab.math.univ-paris-diderot.fr/-/project/996/uploads/9417c336e556b40905375981c1baee1b/dedekind-weighted-automata.pdf","publisher-place":"Marne-la-Vallée, France","title":"Learning weighted automata over number rings, concretely and categorically","type":"speech","URL":"https://www-igm.univ-mlv.fr/~marsault/daal2025/"}

@unpublished{aristoteLearningWeightedAutomata2025d,
  author = {Aristote, Quentin},
  title = {Learning Weighted Automata over Number Rings, Concretely (and
    Categorically)},
  date = {2025-05-09},
  address = {Paris, France},
  url = {https://www.irif.fr/seminaires/automates/index},
  langid = {en},
  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 teaser of how this generalizes to a generic
    reduction procedure between active learning problems for automata
    valued in different categories. These categorical aspects will be
    further developed on May 15th for a talk at the AutCat seminar.}
}

@unpublished{aristoteLearningWeightedAutomata2025d,
  author = {Aristote, Quentin},
  title = {Learning Weighted Automata over Number Rings, Concretely (and
    Categorically)},
  year = {2025},
  month = {may},
  address = {Paris, France},
  url = {https://www.irif.fr/seminaires/automates/index}
}

{"id":"aristoteLearningWeightedAutomata2025d","abstract":"We study automata weighted over number rings, that is, rings of integers in an algebraic number field.\n\nWe 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.\n\nWe 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.\n\nFinally, 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 teaser of how this generalizes to a generic reduction procedure between active learning problems for automata valued in different categories. These categorical aspects will be further developed on May 15th for a talk at the AutCat seminar.","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteLearningWeightedAutomata2025d","event-place":"Paris, France","event-title":"Séminaire Automates (IRIF)","genre":"seminar","issued":{"date-parts":[["2025",5,9]]},"language":"en","note":"slides: https://gitlab.math.univ-paris-diderot.fr/-/project/996/uploads/8b14ed9a7383f9776fc69aa03003890a/dedekind-weighted-automata.pdf","publisher-place":"Paris, France","title":"Learning weighted automata over number rings, concretely (and categorically)","type":"speech","URL":"https://www.irif.fr/seminaires/automates/index"}

@unpublished{aristoteMonotoneWeakDistributive2025c,
  author = {Aristote, Quentin},
  title = {Monotone Weak Distributive Laws in Categories of Algebras},
  date = {2025-04-08},
  address = {Palaiseau, France},
  url = {https://www.lix.polytechnique.fr/proofs-algorithms/tcs/},
  langid = {en},
  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}
}

@unpublished{aristoteMonotoneWeakDistributive2025c,
  author = {Aristote, Quentin},
  title = {Monotone Weak Distributive Laws in Categories of Algebras},
  year = {2025},
  month = {apr},
  address = {Palaiseau, France},
  url = {https://www.lix.polytechnique.fr/proofs-algorithms/tcs/}
}

{"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.\n\nMonotone 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.\n\n[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":{"date-parts":[["2025",4,8]]},"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/"}

@unpublished{aristoteLearningWeightedAutomata2025b,
  author = {Aristote, Quentin},
  title = {Learning Weighted Automata over Number Rings, (Concretely
    and) Categorically},
  date = {2025-03-31},
  address = {Wadern, Germany},
  url = {https://www.dagstuhl.de/25141},
  langid = {en},
  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.}
}

@unpublished{aristoteLearningWeightedAutomata2025b,
  author = {Aristote, Quentin},
  title = {Learning Weighted Automata over Number Rings, (Concretely
    and) Categorically},
  year = {2025},
  month = {mar},
  address = {Wadern, Germany},
  url = {https://www.dagstuhl.de/25141}
}

{"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. \n\nAs 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":{"date-parts":[["2025",3,31]]},"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"}

@unpublished{aristoteLearningWeightedAutomata2025a,
  author = {Aristote, Quentin},
  title = {Learning Weighted Automata over Number Rings, Concretely (and
    Categorically)},
  date = {2025-03-28},
  address = {Marseille, France},
  url = {https://move.lis-lab.fr/seminars},
  langid = {en},
  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.}
}

@unpublished{aristoteLearningWeightedAutomata2025a,
  author = {Aristote, Quentin},
  title = {Learning Weighted Automata over Number Rings, Concretely (and
    Categorically)},
  year = {2025},
  month = {mar},
  address = {Marseille, France},
  url = {https://move.lis-lab.fr/seminars}
}

{"id":"aristoteLearningWeightedAutomata2025a","abstract":"We study automata weighted over number rings, that is, rings of integers in an algebraic number field.\n\nWe 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.\n\nWe 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.\n\nFinally, 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":{"date-parts":[["2025",3,28]]},"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"}

@unpublished{aristoteMonotoneWeakDistributive2025b,
  author = {Aristote, Quentin},
  title = {Monotone Weak Distributive Laws over the Lifted Powerset
    Monad in Categories of Algebras},
  date = {2025-03-27},
  address = {Marseille, France},
  url = {https://lsc.lis-lab.fr/lsc-seminar/},
  langid = {en},
  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.}
}

@unpublished{aristoteMonotoneWeakDistributive2025b,
  author = {Aristote, Quentin},
  title = {Monotone Weak Distributive Laws over the Lifted Powerset
    Monad in Categories of Algebras},
  year = {2025},
  month = {mar},
  address = {Marseille, France},
  url = {https://lsc.lis-lab.fr/lsc-seminar/}
}

{"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.\n\nIn 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.\n\nMore 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":{"date-parts":[["2025",3,27]]},"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/"}

@unpublished{aristoteMonotoneWeakDistributive2025a,
  author = {Aristote, Quentin},
  title = {Monotone Weak Distributive Laws over the Lifted Powerset
    Monad in Categories of Algebras},
  date = {2025-03-05},
  address = {Jena, Germany},
  url = {https://stacs2025.de/},
  langid = {en},
  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.}
}

@unpublished{aristoteMonotoneWeakDistributive2025a,
  author = {Aristote, Quentin},
  title = {Monotone Weak Distributive Laws over the Lifted Powerset
    Monad in Categories of Algebras},
  year = {2025},
  month = {mar},
  address = {Jena, Germany},
  url = {https://stacs2025.de/}
}

{"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":{"date-parts":[["2025",3,5]]},"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/"}

@unpublished{aristoteMonotoneWeakDistributive2024a,
  author = {Aristote, Quentin},
  title = {Monotone Weak Distributive Laws over the Lifted Powerset
    Monad in Categories of Algebras},
  date = {2024-11-15},
  address = {Leiden, Netherlands},
  url = {https://dutchcats.github.io/PSSL-2024/},
  langid = {en},
  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.}
}

@unpublished{aristoteMonotoneWeakDistributive2024a,
  author = {Aristote, Quentin},
  title = {Monotone Weak Distributive Laws over the Lifted Powerset
    Monad in Categories of Algebras},
  year = {2024},
  month = {nov},
  address = {Leiden, Netherlands},
  url = {https://dutchcats.github.io/PSSL-2024/}
}

{"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, Netherlands","event-title":"109th Peripatetic Seminar on Sheaves and Logic (PSSL 109)","genre":"conference","issued":{"date-parts":[["2024",11,15]]},"language":"en","note":"slides: https://dutchcats.github.io/PSSL-2024/slides_PSSL24/Aristote-PSSL109.pdf","publisher-place":"Leiden, Netherlands","title":"Monotone weak distributive laws over the lifted powerset monad in categories of algebras","type":"speech","URL":"https://dutchcats.github.io/PSSL-2024/"}

@unpublished{aristoteMulticategoricalFrameworkMinimization2024,
  author = {Aristote, Quentin},
  title = {Multicategorical Framework for Minimization and Learning of
    Bottom-up Tree Automata with Effects},
  date = {2024-09-18},
  address = {Bordeaux, France},
  url = {https://highlights-conference.org/2024/},
  langid = {en},
  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 principal ideal domains (PIDs).}
}

@unpublished{aristoteMulticategoricalFrameworkMinimization2024,
  author = {Aristote, Quentin},
  title = {Multicategorical Framework for Minimization and Learning of
    Bottom-up Tree Automata with Effects},
  year = {2024},
  month = {sep},
  address = {Bordeaux, France},
  url = {https://highlights-conference.org/2024/}
}

{"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 principal 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":{"date-parts":[["2024",9,18]]},"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/"}

@unpublished{aristoteWeakDistributiveLaws2024,
  author = {Aristote, Quentin},
  title = {Weak Distributive Laws Between Powerspaces over Stably
    Compact Spaces},
  date = {2024-07-04},
  address = {Barcelona, Spain},
  url = {https://iiia.csic.es/tacl2024/},
  langid = {en},
  abstract = {https://iiia.csic.es/tacl2024/abstracts/conference/contributed/TACL\_2024\_paper\_118.pdf}
}

@unpublished{aristoteWeakDistributiveLaws2024,
  author = {Aristote, Quentin},
  title = {Weak Distributive Laws Between Powerspaces over Stably
    Compact Spaces},
  year = {2024},
  month = {jul},
  address = {Barcelona, Spain},
  url = {https://iiia.csic.es/tacl2024/}
}

{"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":{"date-parts":[["2024",7,4]]},"language":"en","note":"slides: https://gitlab.math.univ-paris-diderot.fr/-/project/1057/uploads/a2a13506a3034d6713fa0786adbc9ebf/wdl-powerspaces-scs.pdf\nabstract: 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/"}

@unpublished{aristoteActiveLearningDeterministic2024c,
  author = {Aristote, Quentin},
  title = {Active Learning of Deterministic Transducers with Outputs in
    Arbitrary Monoids},
  date = {2024-06-17},
  address = {Oxford, United Kingdom},
  url = {https://www.cs.ox.ac.uk/research/verification/},
  langid = {en},
  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.}
}

@unpublished{aristoteActiveLearningDeterministic2024c,
  author = {Aristote, Quentin},
  title = {Active Learning of Deterministic Transducers with Outputs in
    Arbitrary Monoids},
  year = {2024},
  month = {jun},
  address = {Oxford, United Kingdom},
  url = {https://www.cs.ox.ac.uk/research/verification/}
}

{"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":{"date-parts":[["2024",6,17]]},"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/"}

@unpublished{aristoteActiveLearningDeterministic2024b,
  author = {Aristote, Quentin},
  title = {Active Learning of Deterministic Transducers with Outputs in
    Arbitrary Monoids},
  date = {2024-03-22},
  address = {Paris, France},
  url = {https://www.irif.fr/seminaires/automates/index},
  langid = {en},
  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.}
}

@unpublished{aristoteActiveLearningDeterministic2024b,
  author = {Aristote, Quentin},
  title = {Active Learning of Deterministic Transducers with Outputs in
    Arbitrary Monoids},
  year = {2024},
  month = {mar},
  address = {Paris, France},
  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":{"date-parts":[["2024",3,22]]},"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"}

@unpublished{aristoteActiveLearningDeterministic2024a,
  author = {Aristote, Quentin},
  title = {Active Learning of Deterministic Transducers with Outputs in
    Arbitrary Monoids},
  date = {2024-02-22},
  address = {Naples, Italy},
  url = {https://www.irif.fr/seminaires/automates/index},
  langid = {en},
  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.}
}

@unpublished{aristoteActiveLearningDeterministic2024a,
  author = {Aristote, Quentin},
  title = {Active Learning of Deterministic Transducers with Outputs in
    Arbitrary Monoids},
  year = {2024},
  month = {feb},
  address = {Naples, Italy},
  url = {https://www.irif.fr/seminaires/automates/index}
}

{"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":{"date-parts":[["2024",2,22]]},"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"}

@unpublished{aristoteAutomataWeightedCommutative2023,
  author = {Aristote, Quentin},
  title = {Automata Weighted over Commutative Rings: Notions of
    Minimality and the Case of {Dedekind} Domains},
  date = {2023-12-06},
  address = {Paris, France},
  url = {https://www.irif.fr/poles/asv/journee_pole_2023},
  langid = {en}
}

@unpublished{aristoteAutomataWeightedCommutative2023,
  author = {Aristote, Quentin},
  title = {Automata Weighted over Commutative Rings: Notions of
    Minimality and the Case of {Dedekind} Domains},
  year = {2023},
  month = {dec},
  address = {Paris, France},
  url = {https://www.irif.fr/poles/asv/journee_pole_2023}
}

{"id":"aristoteAutomataWeightedCommutative2023","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteAutomataWeightedCommutative2023","event-place":"Paris, France","event-title":"ASV day (IRIF)","genre":"seminar","issued":{"date-parts":[["2023",12,6]]},"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"}