About me


Quentin Aristote

Quentin Aristote

Theoretical Computer Science student
@ École Normale Supérieure

e-mail
quentin.aristote@ens.fr (academic)
quentin@aristote.fr (personal)
keys
DFC1660846EEA97C059F18534EF515441E635D36
address
45 rue d'Ulm
75230 CEDEX 05 Paris
online
Git: ENS IRIF personal
LinkedIn
I am a student at the Computer Science Department (DI) of the École Normale Supérieure, an institution part of PSL University. I am mainly interested in applying abstract mathematical theories (e.g. category theory) to computer science in order to get new results for free. I am also interested in practical computer science and enjoy programming using functional languages as well as tinkering with systems.

Publications

Applications of a categorical framework for minimization and active learning of transition systems (2022)
More
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.
Cite.
BibLaTeX
@report{aristoteApplicationsCategoricalFramework2022,
  author = {Aristote, Quentin},
  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.}
}
BibTeX
@techreport{aristoteApplicationsCategoricalFramework2022,
  author = {Aristote, Quentin},
  title = {Applications of a Categorical Framework for Minimization and
    Active Learning of Transition Systems},
  year = {2022},
  month = {aug}
}
CSL JSON
[
  {
    "URL": "https://git.eleves.ens.fr/qaristote/m2-internship-report/uploads/2594114883f26d77c2b4f3731656351a/report.pdf",
    "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",
    "id": "aristoteApplicationsCategoricalFramework2022",
    "issued": {
      "date-parts": [
        [
          2022,
          8,
          20
        ]
      ]
    },
    "language": "en",
    "license": "All rights reserved",
    "title": "Applications of a categorical framework for minimization and active learning of transition systems",
    "type": "report"
  }
]
Fibrational Framework for Nested Alternating Fixed Points and (Bi)Simulation Notions for Büchi Automata (2020)
More
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.
Cite.
BibLaTeX
@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.}
}
BibTeX
@techreport{aristoteFibrationalFrameworkNested2020,
  author = {Aristote, Quentin},
  title = {Fibrational {Framework} for {Nested} {Alternating} {Fixed}
    {Points} and {(Bi)Simulation} {Notions} for {Büchi} {Automata}},
  year = {2020},
  month = {aug}
}
CSL JSON
[
  {
    "URL": "https://git.eleves.ens.fr/qaristote/m1-internship-report/uploads/3431548a277eb5fc297d8e7d93d1e3ce/aristote_quentin_m1_internship_report.pdf",
    "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",
    "id": "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"
  }
]
Dynamical Triangulation Induced by Quantum Walk (2020)
With Nathanaël Eon, Giuseppe Di Molfetta. In Symmetry, 12, 1:128, Multidisciplinary Digital Publishing Institute. ISSN: 2073-8994. DOI: 10.3390/sym12010128
More
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.
Cite.
BibLaTeX
@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.}
}
BibTeX
@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}
}
CSL JSON
[
  {
    "DOI": "10.3390/sym12010128",
    "ISSN": "2073-8994",
    "URL": "https://www.mdpi.com/2073-8994/12/1/128",
    "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": "Di Molfetta",
        "given": "Giuseppe"
      }
    ],
    "citation-key": "aristoteDynamicalTriangulationInduced2020",
    "container-title": "Symmetry",
    "id": "aristoteDynamicalTriangulationInduced2020",
    "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",
    "source": "www.mdpi.com",
    "title": "Dynamical Triangulation Induced by Quantum Walk",
    "type": "article-journal",
    "volume": "12"
  }
]
Marche quantique sur un réseau triangulaire sujet à des Pachner moves (2019)
More
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.
Cite.
BibLaTeX
@report{aristoteMarcheQuantiqueReseau2019,
  author = {Aristote, Quentin},
  title = {Marche quantique sur un réseau triangulaire sujet à des
    Pachner moves},
  pages = {15},
  date = {2019-08-25},
  url = {https://git.eleves.ens.fr/qaristote/rapport-stage-l3/-/raw/b9f9cc78ad3eabe6508be70cc27dc9bf89d34755/rapport.pdf},
  langid = {fr},
  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) -
    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.}
}
BibTeX
@techreport{aristoteMarcheQuantiqueReseau2019,
  author = {Aristote, Quentin},
  title = {{Marche quantique sur un réseau triangulaire sujet à des
    Pachner moves}},
  pages = {15},
  year = {2019},
  month = {aug}
}
CSL JSON
[
  {
    "URL": "https://git.eleves.ens.fr/qaristote/rapport-stage-l3/-/raw/b9f9cc78ad3eabe6508be70cc27dc9bf89d34755/rapport.pdf",
    "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",
    "id": "aristoteMarcheQuantiqueReseau2019",
    "issued": {
      "date-parts": [
        [
          2019,
          8,
          25
        ]
      ]
    },
    "language": "fr",
    "license": "All rights reserved",
    "page": "15",
    "title": "Marche quantique sur un réseau triangulaire sujet à des Pachner moves",
    "type": "report"
  }
]

Software

bibli-paris
Spacemacs layer that adds functionnalities to org-mode, allowing for managing reading lists of documents from Paris’ network of libraries.
smtlib-backends
Haskell library providing low-level functions for SMT-LIB-based interaction with SMT solvers.
webpage
Nix-based static webpage generator.

Experience

Software Engineering intern @ Tweag, Paris, France
-
Ongoing. Speeding-up Pirouette (a symbolic evaluator using incorrectness logic) by optimizing its interactions with SMT solvers.
research intern in Applied Category Theory @ IRIF (UMR 8243), CNRS, Paris, France
- · supervised by Daniela Petrişan · internship report
Studied a categorical framework for the minimization and active learning of transition systems.
research intern in Applied Category Theory @ ERATO MMSD, NII, Tōkyō, Japan
- · supervised by Ichiro Hasuo Jérémy Dubut · internship report
Studied a fibrational framework for nested fixed points and (bi)simulation notions for Büchi automata.
research intern in Natural Computing @ LiS Laboratory (UMR 7020), CNRS, Luminy, France
- · supervised by Giuseppe di Molfetta · internship report paper
Studied a quantum walker whose density changes its own environment.

Education

Master's degree in Theoretical Computer Science @ École Normale Supérieure, Paris, France
-
Second year Master's degree in Theoretical Computer Science @ MPRI
-
Graduated with highest honors (18.43/20), second of a highly-selective class of 70 students.
Computer Science courses Approximation Algorithms · Concurrency · Denotational Semantics (Domains, Categories, Games) · Finite Automata as Models · Functional Programmming & Type Systems · Game Theory · Molecular Algorithms · Non-Sequential Theory of Distributed Systems · Probabilistic Programming · Programming Shared-Memory Multi-Threaded Machines · Proof Assistants · Proof Systems · Proof of Programs · Quantum Computing · Real-time & Hybrid Systems · Well Quasi-Orders & Algorithms
First year Master's degree in Computer Science @ DIENS
-
Completed with highest honors (18.20/20).
Computer Science courses Artificial Vision · Combinatorial & Convex Optimisation · Deep Learning · Lambda Calculus & Categories · Models & Algorithms for Networks · Parallel & Reactive Programming · Path Planning in Robotics · Random Structures & Algorithms
Mathematics courses Algebra (Domains) · Algebraic Topology · Data Science · Differential Geometry · Dynamical Systems · Functional Analysis · Logics · Partial Differential Equations · Statistics · Stochastic Processes
Bachelor's degrees in Computer Science and Mathematics @ DIENS
-
Graduated with highest honors in Computer Science (17.80/20), with honors in Mathematics (14.74/20)
Computer Science courses Algorithms & Programming · Cryptography · Databases · Formal Languages, Decidability & Complexity · Hardware Systems · Machine Learning · Operating Systems · Programming Languages & Compilation · Semantics & Verification of Programs
Mathematics courses Algebra (Groups) · Complex Analysis · Information Theory · Measure Theory · Topology & Differential Calculus
Took two gap years: one to follow additional postgraduate courses in Mathematics; one to do additional internships.
Higher Schools Preparatory Classes @ Lycée Louis-le-Grand, Paris, France
-
MPSI - MP* (Mathematics, Physics & Computer Science)