---
references:
- 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:
    - year: 2022
      month: 8
      day: 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

- 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:
    - year: 2020
      month: 8
      day: 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

- 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.

    Des 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:
    - year: 2019
      month: 8
      day: 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
...