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authoraristote <quentin.aristote@irif.fr>2025-07-27 12:15:34 +0200
committeraristote <quentin.aristote@irif.fr>2025-07-27 13:07:02 +0200
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----
-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
-...