@inproceedings{aristoteMonotoneWeakDistributive2025,
  author = {Aristote, Quentin},
  editor = {Beyersdorff, Olaf and Pilipczuk, Michał and Pimentel, Elaine
    and Thắng, Nguyễn Kim},
  publisher = {Schloss Dagstuhl – Leibniz-Zentrum für Informatik},
  title = {Monotone {Weak} {Distributive} {Laws} over the {Lifted}
    {Powerset} {Monad} in {Categories} of {Algebras}},
  booktitle = {42nd International Symposium on Theoretical Aspects of
    Computer Science (STACS 2025)},
  series = {Leibniz International Proceedings in Informatics (LIPIcs)},
  volume = {327},
  pages = {10:1–10:20},
  date = {2025},
  urldate = {2025-02-25},
  address = {Dagstuhl, Germany},
  url = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.10},
  doi = {10.4230/LIPIcs.STACS.2025.10},
  isbn = {978-3-95977-365-2},
  issn = {1868-8969},
  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.}
}

@inproceedings{aristoteMonotoneWeakDistributive2025,
  author = {Aristote, Quentin},
  editor = {Beyersdorff, Olaf and Pilipczuk, Michał and Pimentel, Elaine
    and Thắng, Nguyễn Kim},
  publisher = {Schloss Dagstuhl – Leibniz-Zentrum für Informatik},
  title = {Monotone {Weak} {Distributive} {Laws} over the {Lifted}
    {Powerset} {Monad} in {Categories} of {Algebras}},
  booktitle = {42nd International Symposium on Theoretical Aspects of
    Computer Science (STACS 2025)},
  series = {Leibniz International Proceedings in Informatics (LIPIcs)},
  volume = {327},
  pages = {10:1–10:20},
  year = {2025},
  address = {Dagstuhl, Germany},
  url = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.10}
}

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@inproceedings{aristoteActiveLearningDeterministic2024,
  author = {Aristote, Quentin},
  publisher = {Schloss-Dagstuhl - Leibniz Zentrum für Informatik},
  title = {Active {Learning} of {Deterministic} {Transducers} with
    {Outputs} in {Arbitrary} {Monoids}},
  booktitle = {32nd EACSL Annual Conference on Computer Science Logic
    (CSL 2024)},
  series = {Leibniz International Proceedings in Informatics (LIPIcs)},
  volume = {288},
  pages = {11:1-11:20},
  date = {2024},
  urldate = {2024-02-07},
  address = {Dagstuhl, Germany},
  url = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2024.11},
  doi = {10.4230/LIPIcs.CSL.2024.11},
  isbn = {978-3-95977-310-2},
  issn = {1868-8969},
  note = {Helena Rasiowa award for the Best Student Paper},
  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.}
}

@inproceedings{aristoteActiveLearningDeterministic2024,
  author = {Aristote, Quentin},
  publisher = {Schloss-Dagstuhl - Leibniz Zentrum für Informatik},
  title = {Active {Learning} of {Deterministic} {Transducers} with
    {Outputs} in {Arbitrary} {Monoids}},
  booktitle = {32nd EACSL Annual Conference on Computer Science Logic
    (CSL 2024)},
  series = {Leibniz International Proceedings in Informatics (LIPIcs)},
  volume = {288},
  pages = {11:1-11:20},
  year = {2024},
  address = {Dagstuhl, Germany},
  note = {Helena Rasiowa award for the Best Student Paper},
  url = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2024.11}
}

{"id":"aristoteActiveLearningDeterministic2024","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.","accessed":{"date-parts":[["2024",2,7]]},"author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteActiveLearningDeterministic2024","collection-title":"Leibniz International Proceedings in Informatics (LIPIcs)","container-title":"32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)","DOI":"10.4230/LIPIcs.CSL.2024.11","event-place":"Dagstuhl, Germany","event-title":"Computer Science Logic (CSL)","ISBN":"978-3-95977-310-2","ISSN":"1868-8969","issued":{"date-parts":[["2024"]]},"language":"en","note":"Helena Rasiowa award for the Best Student Paper","page":"11:1-11:20","publisher":"Schloss-Dagstuhl - Leibniz Zentrum für Informatik","publisher-place":"Dagstuhl, Germany","title":"Active Learning of Deterministic Transducers with Outputs in Arbitrary Monoids","type":"paper-conference","URL":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2024.11","volume":"288"}

@unpublished{aristoteMonotoneWeakDistributive2024,
  author = {Aristote, Quentin},
  title = {Monotone Weak Distributive Laws over the Lifted Powerset
    Monad in Categories of Algebras},
  date = {2024-10},
  urldate = {2024-11-04},
  url = {https://hal.science/hal-04712728v4},
  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{aristoteMonotoneWeakDistributive2024,
  author = {Aristote, Quentin},
  title = {Monotone Weak Distributive Laws over the Lifted Powerset
    Monad in Categories of Algebras},
  year = {2024},
  month = {oct},
  url = {https://hal.science/hal-04712728v4}
}

{"id":"aristoteMonotoneWeakDistributive2024","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.","accessed":{"date-parts":[["2024",11,4]]},"author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteMonotoneWeakDistributive2024","issued":{"date-parts":[["2024",10]]},"language":"en","title":"Monotone weak distributive laws over the lifted powerset monad in categories of algebras","type":"manuscript","URL":"https://hal.science/hal-04712728v4"}

@misc{aristoteFunctorialApproachMinimizing2023,
  author = {Aristote, Quentin},
  publisher = {HAL},
  title = {Functorial Approach to Minimizing and Learning Deterministic
    Transducers with Outputs in Arbitrary Monoids},
  number = {04172251},
  date = {2023-07-27},
  urldate = {2023-07-27},
  url = {https://hal.science/hal-04172251},
  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. We also extend
    the framework with a categorical algorithm for minimizing transition
    systems, whose instantiation retrieves the algorithm for minimizing
    monoidal transducers but also extends the class of output monoids
    for which this algorithm is valid.}
}

@misc{aristoteFunctorialApproachMinimizing2023,
  author = {Aristote, Quentin},
  publisher = {HAL},
  title = {Functorial Approach to Minimizing and Learning Deterministic
    Transducers with Outputs in Arbitrary Monoids},
  number = {04172251},
  year = {2023},
  month = {jul},
  url = {https://hal.science/hal-04172251}
}

{"id":"aristoteFunctorialApproachMinimizing2023","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. We also extend the framework with a categorical algorithm for minimizing transition systems, whose instantiation retrieves the algorithm for minimizing monoidal transducers but also extends the class of output monoids for which this algorithm is valid.","accessed":{"date-parts":[["2023",7,27]]},"author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteFunctorialApproachMinimizing2023","issued":{"date-parts":[["2023",7,27]]},"language":"en","number":"04172251","publisher":"HAL","title":"Functorial approach to minimizing and learning deterministic transducers with outputs in arbitrary monoids","type":"article","URL":"https://hal.science/hal-04172251"}

@misc{aristoteSmtlibbackendsFasterSMTLIBbased2023,
  author = {Aristote, Quentin},
  title = {Smtlib-Backends: Faster {SMT-LIB-based} {Haskell} Interface
    to {SMT} Solvers},
  date = {2023-02-14},
  url = {https://www.tweag.io/blog/2023-02-14-smtlib-backends},
  langid = {en},
  abstract = {Announcement of smtlib-backends, a Haskell library
    providing a generic interface for interacting with SMT solvers using
    SMT-LIB.}
}

@misc{aristoteSmtlibbackendsFasterSMTLIBbased2023,
  author = {Aristote, Quentin},
  title = {Smtlib-Backends: Faster {SMT-LIB-based} {Haskell} Interface
    to {SMT} Solvers},
  year = {2023},
  month = {feb},
  url = {https://www.tweag.io/blog/2023-02-14-smtlib-backends}
}

{"id":"aristoteSmtlibbackendsFasterSMTLIBbased2023","abstract":"Announcement of smtlib-backends, a Haskell library providing a generic interface for interacting with SMT solvers using SMT-LIB.","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteSmtlibbackendsFasterSMTLIBbased2023","container-title":"Tweag Blog","issued":{"date-parts":[["2023",2,14]]},"language":"en","title":"smtlib-backends: faster SMT-LIB-based Haskell interface to SMT solvers","title-short":"smtlib-backends","type":"post-weblog","URL":"https://www.tweag.io/blog/2023-02-14-smtlib-backends"}

@report{aristoteApplicationsCategoricalFramework2022,
  author = {Aristote, Quentin},
  publisher = {École Normale Supérieure, PSL University},
  title = {Applications of a Categorical Framework for Minimization and
    Active Learning of Transition Systems},
  date = {2022-08-20},
  url = {https://git.eleves.ens.fr/qaristote/m2-internship-report/uploads/2594114883f26d77c2b4f3731656351a/report.pdf},
  langid = {en},
  abstract = {M2 internship report. We extend Petrişan and Colcombet’s
    categorical framework for automata minimization and learning with
    new categorical algorithms and apply it to various families of
    automata for which minimization and learning had not been studied
    previously. We focus on transducers whose output lie in arbitrary
    monoids, weighted automata on Dedekind domains and automata whose
    states are quasi-ordered. This last example links automata learning
    together with the Valk-Jantzen lemma, widely used in the theory of
    well-structured transition systems.}
}

@techreport{aristoteApplicationsCategoricalFramework2022,
  author = {Aristote, Quentin},
  publisher = {École Normale Supérieure, PSL University},
  title = {Applications of a Categorical Framework for Minimization and
    Active Learning of Transition Systems},
  year = {2022},
  month = {aug},
  url = {https://git.eleves.ens.fr/qaristote/m2-internship-report/uploads/2594114883f26d77c2b4f3731656351a/report.pdf}
}

{"id":"aristoteApplicationsCategoricalFramework2022","abstract":"M2 internship report. We extend Petrişan and Colcombet's categorical framework for automata minimization and learning with new categorical algorithms and apply it to various families of automata for which minimization and learning had not been studied previously. We focus on transducers whose output lie in arbitrary monoids, weighted automata on Dedekind domains and automata whose states are quasi-ordered. This last example links automata learning together with the Valk-Jantzen lemma, widely used in the theory of well-structured transition systems.","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteApplicationsCategoricalFramework2022","issued":{"date-parts":[["2022",8,20]]},"language":"en","license":"All rights reserved","publisher":"École Normale Supérieure, PSL University","title":"Applications of a categorical framework for minimization and active learning of transition systems","type":"report","URL":"https://git.eleves.ens.fr/qaristote/m2-internship-report/uploads/2594114883f26d77c2b4f3731656351a/report.pdf"}

@report{aristoteFibrationalFrameworkNested2020,
  author = {Aristote, Quentin},
  title = {Fibrational {Framework} for {Nested} {Alternating} {Fixed}
    {Points} and {(Bi)Simulation} {Notions} for {Büchi} {Automata}},
  date = {2020-08-28},
  url = {https://git.eleves.ens.fr/qaristote/m1-internship-report/uploads/3431548a277eb5fc297d8e7d93d1e3ce/aristote_quentin_m1_internship_report.pdf},
  langid = {en},
  abstract = {M1 internship report. We extend a previous fibration- and
    coalgebra-based categorical framework for characterizing greatest
    fixed-points, e.g. bisimilarity-like notions, as winning positions
    in safety games. Our new framework thus characterizes nested
    alternating greatest and smallest fixed-points of a fibration- and
    coalgebra-based categorical operator as winning positions in parity
    games. This provides a new kind of parity games for the model
    checking of coalgebraic modal logic, but unfortunately we did not
    manage to instantiate more general notions of bisimulations such as
    fair and delayed bisimulations.}
}

@techreport{aristoteFibrationalFrameworkNested2020,
  author = {Aristote, Quentin},
  title = {Fibrational {Framework} for {Nested} {Alternating} {Fixed}
    {Points} and {(Bi)Simulation} {Notions} for {Büchi} {Automata}},
  year = {2020},
  month = {aug},
  url = {https://git.eleves.ens.fr/qaristote/m1-internship-report/uploads/3431548a277eb5fc297d8e7d93d1e3ce/aristote_quentin_m1_internship_report.pdf}
}

{"id":"aristoteFibrationalFrameworkNested2020","abstract":"M1 internship report. We extend a previous fibration- and coalgebra-based categorical framework for characterizing greatest fixed-points, e.g. bisimilarity-like notions, as winning positions in safety games. Our new framework thus characterizes nested alternating greatest and smallest fixed-points of a fibration- and coalgebra-based categorical operator as winning positions in parity games. This provides a new kind of parity games for the model checking of coalgebraic modal logic, but unfortunately we did not manage to instantiate more general notions of bisimulations such as fair and delayed bisimulations.","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteFibrationalFrameworkNested2020","issued":{"date-parts":[["2020",8,28]]},"language":"en","license":"All rights reserved","title":"Fibrational Framework for Nested Alternating Fixed Points and (Bi)Simulation Notions for Büchi Automata","type":"report","URL":"https://git.eleves.ens.fr/qaristote/m1-internship-report/uploads/3431548a277eb5fc297d8e7d93d1e3ce/aristote_quentin_m1_internship_report.pdf"}

@article{aristoteDynamicalTriangulationInduced2020,
  author = {Aristote, Quentin and Eon, Nathanaël and di Molfetta,
    Giuseppe},
  publisher = {Multidisciplinary Digital Publishing Institute},
  title = {Dynamical {Triangulation} {Induced} by {Quantum} {Walk}},
  journal = {Symmetry},
  volume = {12},
  number = {1},
  date = {2020-01},
  urldate = {2020-08-17},
  url = {https://www.mdpi.com/2073-8994/12/1/128},
  doi = {10.3390/sym12010128},
  issn = {2073-8994},
  langid = {en},
  abstract = {We present the single-particle sector of a quantum
    cellular automaton, namely a quantum walk, on a simple dynamical
    triangulated 2-manifold. The triangulation is changed through
    Pachner moves, induced by the walker density itself, allowing the
    surface to transform into any topologically equivalent one. This
    model extends the quantum walk over triangular grid, introduced in a
    previous work, by one of the authors, whose space-time limit
    recovers the Dirac equation in (2+1)-dimensions. Numerical
    simulations show that the number of triangles and the local
    curvature grow as exp(a log(t) - bt\textsuperscript{2}), where a and
    b parametrize the way geometry changes upon the local density of the
    walker, and that, in the long run, flatness emerges. Finally, we
    also prove that the global behavior of the walker, remains the same
    under spacetime random fluctuations.}
}

@article{aristoteDynamicalTriangulationInduced2020,
  author = {Aristote, Quentin and Eon, Nathanaël and di Molfetta,
    Giuseppe},
  publisher = {Multidisciplinary Digital Publishing Institute},
  title = {Dynamical {Triangulation} {Induced} by {Quantum} {Walk}},
  journal = {Symmetry},
  volume = {12},
  number = {1},
  year = {2020},
  month = {jan},
  url = {https://www.mdpi.com/2073-8994/12/1/128}
}

{"id":"aristoteDynamicalTriangulationInduced2020","abstract":"We present the single-particle sector of a quantum cellular automaton, namely a quantum walk, on a simple dynamical triangulated 2-manifold. The triangulation is changed through Pachner moves, induced by the walker density itself, allowing the surface to transform into any topologically equivalent one. This model extends the quantum walk over triangular grid, introduced in a previous work, by one of the authors, whose space-time limit recovers the Dirac equation in (2+1)-dimensions. Numerical simulations show that the number of triangles and the local curvature grow as exp(a log(t) - bt²), where a and b parametrize the way geometry changes upon the local density of the walker, and that, in the long run, flatness emerges. Finally, we also prove that the global behavior of the walker, remains the same under spacetime random fluctuations.","accessed":{"date-parts":[["2020",8,17]]},"author":[{"family":"Aristote","given":"Quentin"},{"family":"Eon","given":"Nathanaël"},{"family":"Molfetta","given":"Giuseppe","non-dropping-particle":"di"}],"citation-key":"aristoteDynamicalTriangulationInduced2020","container-title":"Symmetry","DOI":"10.3390/sym12010128","ISSN":"2073-8994","issue":"1:128","issued":{"date-parts":[["2020",1]]},"language":"en","license":"http://creativecommons.org/licenses/by/3.0/","number":"1","publisher":"Multidisciplinary Digital Publishing Institute","title":"Dynamical Triangulation Induced by Quantum Walk","type":"article-journal","URL":"https://www.mdpi.com/2073-8994/12/1/128","volume":"12"}

@report{aristoteMarcheQuantiqueReseau2019,
  author = {Aristote, Quentin},
  title = {Marche Quantique Sur Un Réseau Triangulaire Sujet à Des
    {Pachner} Moves},
  date = {2019-08-25},
  url = {https://git.eleves.ens.fr/qaristote/rapport-stage-l3/-/raw/b9f9cc78ad3eabe6508be70cc27dc9bf89d34755/rapport.pdf},
  langid = {en},
  abstract = {Rapport de stage de L3. On introduit un automate
    cellulaire quantique à une particule, un marcheur quantique, sur une
    variété triangulée de dimension 2. La triangulation change à travers
    des Pachner moves, induits eux-même par la densité du marcheur,
    permettant à la surface de se transformer en n’importe quelle autre
    surface qui lui est topologiquement équivalente. Ce modèle
    généralise le marcheur quantique sur un réseau triangulaire,
    introduit dans un article précédent par un des auteurs, et dont la
    limite en espace-temps retombe sur l’équation de Dirac en 2+1
    dimensions.nDes simulations numériques montrent que le nombre de
    triangles et que la courbure évoluent en exp(a log(t) -
    bt\textsuperscript{2}), où a et b paramétrisent la façon dont la
    géométrie change selon la densité locale du marcheur, et que, sur le
    long terme, la surface redevient plate. Enfin, on montre aussi
    numériquement que le comportement global du marcheur reste le même
    sous l’influence de fluctuations spatio-temporelles aléatoires.}
}

@techreport{aristoteMarcheQuantiqueReseau2019,
  author = {Aristote, Quentin},
  title = {Marche Quantique Sur Un Réseau Triangulaire Sujet à Des
    {Pachner} Moves},
  year = {2019},
  month = {aug},
  url = {https://git.eleves.ens.fr/qaristote/rapport-stage-l3/-/raw/b9f9cc78ad3eabe6508be70cc27dc9bf89d34755/rapport.pdf}
}

{"id":"aristoteMarcheQuantiqueReseau2019","abstract":"Rapport de stage de L3. On introduit un automate cellulaire quantique à une particule, un marcheur quantique, sur une variété triangulée de dimension 2. La triangulation change à travers des Pachner moves, induits eux-même par la densité du marcheur, permettant à la surface de se transformer en n'importe quelle autre surface qui lui est topologiquement équivalente. Ce modèle généralise le marcheur quantique sur un réseau triangulaire, introduit dans un article précédent par un des auteurs, et dont la limite en espace-temps retombe sur l'équation de Dirac en 2+1 dimensions.nDes simulations numériques montrent que le nombre de triangles et que la courbure évoluent en  exp(a log(t) - bt²), où a et b paramétrisent la façon dont la géométrie change selon la densité locale du marcheur, et que, sur le long terme, la surface redevient plate. Enfin, on montre aussi numériquement que le comportement global du marcheur reste le même sous l'influence de fluctuations spatio-temporelles aléatoires.","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteMarcheQuantiqueReseau2019","issued":{"date-parts":[["2019",8,25]]},"language":"en","license":"All rights reserved","title":"Marche quantique sur un réseau triangulaire sujet à des Pachner moves","type":"report","URL":"https://git.eleves.ens.fr/qaristote/rapport-stage-l3/-/raw/b9f9cc78ad3eabe6508be70cc27dc9bf89d34755/rapport.pdf"}