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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: 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
+...