Jérémy Ledent | Publications

2024

Epistemic Logic
A Many-Sorted Epistemic Logic for Chromatic Hypergraphs

Éric Goubault, Roman Kniazev, and Jérémy Ledent

In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)

Abstract Bibtex URL arXiv PDF

We propose a many-sorted modal logic for reasoning about knowledge in multi-agent systems. Our logic introduces a clear distinction between participating agents and the environment. This allows to express local properties of agents and global properties of worlds in a uniform way, as well as to talk about the presence or absence of agents in a world. The logic subsumes previous attempts at epistemic logic with variable number of agents. The semantics is given in chromatic hypergraphs, a generalization of chromatic simplicial complexes, which were recently used to model knowledge in distributed systems. We show that the logic is sound and complete with respect to the intended semantics. We also show a further connection of chromatic hypergraphs with neighborhood frames.
```
@InProceedings{goubault2023manysorted,
  author =	{Goubault, \'{E}ric and Kniazev, Roman and Ledent, J\'{e}r\'{e}my},
  title =	{{A Many-Sorted Epistemic Logic for Chromatic Hypergraphs}},
  booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
  pages =	{30:1–30:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-310-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{288},
  editor =	{Murano, Aniello and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl – Leibniz-Zentrum f{\ü}r Informatik},
  address =	{Dagstuhl, Germany},
  doi =		{10.4230/LIPIcs.CSL.2024.30},
}
```

2023

Epistemic Logic,
Concurrency

Simplicial Models for the Epistemic Logic of Faulty Agents

Éric Goubault, Roman Kniazev, Jérémy Ledent, and Sergio Rajsbaum

Abstract arXiv PDF

In recent years, several authors have been investigating simplicial models, a model of epistemic logic based on higher-dimensional structures called simplicial complexes. In the original formulation, simplicial models are always assumed to be pure, meaning that all worlds have the same dimension. This is equivalent to the standard S5 semantics of epistemic logic, based on Kripke models. By removing the assumption that models must be pure, we can go beyond the usual Kripke semantics and study epistemic logics where the number of agents participating in a world can vary. This approach has been developed in a number of papers, with applications in fault-tolerant distributed computing where processes may crash during the execution of a system. A difficulty that arises is that subtle design choices in the definition of impure simplicial models can result in different axioms of the resulting logic. In this paper, we classify those design choices systematically, and axiomatize the corresponding logics. We illustrate them via distributed computing examples of synchronous systems where processes may crash.
Epistemic Logic,
Topology
Semi-Simplicial Set Models for Distributed Knowledge

Éric Goubault, Roman Kniazev, Jérémy Ledent, and Sergio Rajsbaum

In 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2023)

Abstract Bibtex URL arXiv Slides More slides

In recent years, a new class of models for multi-agent epistemic logic has emerged, based on simplicial complexes. Since then, many variants of these simplicial models have been investigated, giving rise to different logics and axiomatizations. In this paper, we present a further generalization, which encompasses all previously studied variants of simplicial models. Geometrically, this is achieved by generalizing beyond simplicial complexes, and considering instead semi-simplicial sets. By doing so, we define a new semantics for epistemic logic with distributed knowledge, where a group of agents may distinguish two worlds, even though each individual agent in the group is unable to distinguish them. As it turns out, these models are the geometric counterpart of a generalization of Kripke models, called “pseudo-models”. We show how to recover the previously defined variants of simplicial models as sub-classes of our models; and give a sound and complete axiomatization for each of them.
```
@inproceedings{GoubaultKLR23semisimplicial,
  author       = {{\'{E}}ric Goubault and
                  Roman Kniazev and
                  J{\'{e}}r{\'{e}}my Ledent and
                  Sergio Rajsbaum},
  title        = {Semi-Simplicial Set Models for Distributed Knowledge},
  booktitle    = {38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)},
  pages        = {1–13},
  year         = {2023},
  url          = {https://doi.org/10.1109/LICS56636.2023.10175737},
  doi          = {10.1109/LICS56636.2023.10175737},
}
```

2022

Epistemic Logic
A Simplicial Model for KB4: Epistemic Logic with Agents That May Die

Éric Goubault, Jérémy Ledent, and Sergio Rajsbaum

In 39th International Symposium on Theoretical Aspects of Computer Science, STACS 2022

Abstract Bibtex URL arXiv Slides

The standard semantics of multi-agent epistemic logic S5 is based on Kripke models whose accessibility relations are reflexive, symmetric and transitive. This one dimensional structure contains implicit higher-dimensional information beyond pairwise interactions, that we have formalized as pure simplicial models in previous work. Here we extend the theory to encompass all simplicial models — including the ones that are not pure. The corresponding Kripke models are those where the accessibility relation is symmetric and transitive, but might not be reflexive. This yields the epistemic logic KB4, which can reason about situations where some of the agents may die. We illustrate it through distributed computing examples of synchronous systems where processes may crash.
```
@inproceedings{GoubaultLR21kb4,
  author    = {{\'{E}}ric Goubault and
               J{\'{e}}r{\'{e}}my Ledent and
               Sergio Rajsbaum},
  title     = {A Simplicial Model for KB4{\_}n: Epistemic Logic with Agents That
               May Die},
  booktitle = {39th International Symposium on Theoretical Aspects of Computer Science,
               {STACS} 2022},
  pages     = {33:1–33:20},
  year      = {2022},
  doi       = {10.4230/LIPIcs.STACS.2022.33},
}
```
Infinite games,
Coalgebras
Infinite horizon extensive form games, coalgebraically

Matteo Capucci, Neil Ghani, Clemens Kupke, Jérémy Ledent, and Fredrik Nordvall Forsberg

Mathematics for Computation, 2022

Abstract Bibtex PDF

Extensive form games are possibly infinite trees, whose nodes are decorated by players, and whose branching structure reflects the decisions available to the players at each stage of the game. In the game theory literature, such trees are typically defined in a monolithic, non-compositional way. Instead, we use the theory of coalgebras to give a categorical description of extensive form games. We show the merit of this approach by proving the well-known “ one-shot deviation principle ” in our coalgebraic setting.
```
@inbook{CapucciGKLN21infinite,
  author = "Matteo Capucci and Neil Ghani and Clemens Kupke and J{\'e}r{\'e}my Ledent and {Nordvall Forsberg}, Fredrik",
  title = "Infinite horizon extensive form games, coalgebraically",
  year = "2022",
  booktitle = "Mathematics for Computation",
  publisher = "World Scientific Publishing Co. Pte Ltd",
}
```
Epistemic logic,
Topology
Knowledge and Simplicial Complexes

Hans van Ditmarsch, Éric Goubault, Jérémy Ledent, and Sergio Rajsbaum

In Philosophy of Computing, 2022

Abstract Bibtex URL PDF

Simplicial complexes are a versatile and convenient paradigm on which to buildall the tools and techniques of epistemic logic. Thus, we can define: knowledge, belief, bisimulation, the group notions of mutual, distributed and common knowledge, and also dynamics in the shape of simplicial action models. We give a survey on how to interpret all such notions on simplicial complexes.
```
@inproceedings{DitmarschGLR20knowledge,
  author="Ditmarsch, Hans van and Goubault, {\'E}ric and Ledent, J{\'e}r{\'e}my and Rajsbaum, Sergio",
  editor="Lundgren, Bj{\"o}rn and Nu{\~{n}}ez Hern{\'a}ndez, Nancy Abigail",
  title="Knowledge and Simplicial Complexes",
  booktitle="Philosophy of Computing",
  year="2022",
  publisher="Springer International Publishing",
  address="Cham",
  volume = "143",
  pages="1–50",
  doi = "10.1007/978-3-030-75267-5_1",
  isbn="978-3-030-75267-5",
}
```

2021

Category Theory,
Open Games
Translating Extensive Form Games to Open Games with Agency

Matteo Capucci, Neil Ghani, Jérémy Ledent, and Fredrik Nordvall Forsberg

In 4th international Applied Category Theory Conference, ACT 2021

Abstract Bibtex arXiv PDF

We show open games cover extensive form games with both perfect and imperfect information. Doing so forces us to address two current weaknesses in open games: the lack of a notion of player and their agency within open games, and the lack of choice operators. Using the former we construct the latter, and these choice operators subsume previous proposed operators for open games, thereby making progress towards a core, canonical and ergonomic calculus of game operators. Collectively these innovations increase the level of compositionality of open games, and demonstrate their expressiveness.
```
@inproceedings{CapucciGLN21extensive,
  author    = {Matteo Capucci and
               Neil Ghani and
               J{\'e}r{\'e}my Ledent and
               Fredrik Nordvall Forsberg},
  title     = {Translating Extensive Form Games to Open Games with Agency},
  booktitle = {4th international Applied Category Theory Conference, {ACT} 2021},
  year      = {2021},
  url       = {https://arxiv.org/abs/2105.06763},
}
```
Topology,
Concurrency
Brief Announcement: Variants of Approximate Agreement on Graphs and Simplicial Complexes

Jérémy Ledent

In PODC ’21: ACM Symposium on Principles of Distributed Computing

Abstract Bibtex URL PDF Slides Video

Approximate agreement is a weaker version of consensus where two or more processes must agree on a real number within a distance ε of each other. We focus on two variants of approximate agreement on graphs, known as graph convergence and monophonic approximate agreement. We show that both tasks arise as special cases of a more general, higher-dimensional, approximate agreement task, where the processes must agree on the vertices of a simplex in a given simplicial complex. This new point of view gives rise to a novel topological perspective on the solvability of monophonic approximate agreement.
```
@inproceedings{Ledent21brief,
  author    = {J{\'e}r{\'e}my Ledent},
  title     = {Brief Announcement: Variants of Approximate Agreement on Graphs and Simplicial Complexes},
  booktitle = {{PODC} '21: {ACM} Symposium on Principles of Distributed Computing},
  year      = {2021},
  doi       = {10.1145/3465084.3467946},
}
```
Concurrency,
Epistemic logic
A Dynamic Epistemic Logic analysis of Equality Negation and other Epistemic Covering tasks

Hans van Ditmarsch, Éric Goubault, Marijana Lazić, Jérémy Ledent, and Sergio Rajsbaum

Journal of Logical and Algebraic Methods in Programming, 2021

Abstract Bibtex URL PDF

(This is the journal version of our DaLi’19 paper.)
In this paper we study the solvability of the equality negation task in a simple wait-free model where processes communicate by reading and writing shared variables or exchanging messages. In this task, two processes start with a private input value in the set {0, 1, 2}, and after communicating, each one must decide a binary output value, so that the outputs of the processes are the same if and only if the input values of the processes are different. This task is already known to be unsolvable; our goal here is to prove this result using the Dynamic Epistemic Logic approach introduced in a previous paper [GandALF’18]. We show that in fact, there is no epistemic logic formula that explains why the task is unsolvable. Furthermore, we observe that this task is a particular case of an epistemic covering task. This gives rise to a new topological perspective on the equality negation task, through the lens of the theory of covering spaces.
```
@article{vanDitmarschGLLR21dynamic,
  title = {A Dynamic Epistemic Logic analysis of Equality Negation and other Epistemic Covering tasks},
  author = {Hans {van Ditmarsch} and
            {{\'{E}}ric Goubault and
            Marijana Lazi\'{c} and
            J{\'{e}}r{\'{e}}my Ledent and
            Sergio Rajsbaum
  },
  journal = {Journal of Logical and Algebraic Methods in Programming},
  volume = {121},
  pages = {100662},
  year = {2021},
  issn = {2352-2208},
  doi = {10.1016/j.jlamp.2021.100662},
}
```
Concurrency,
Epistemic logic
A Simplicial Complex Model for Dynamic Epistemic Logic to study Distributed Task Computability

Éric Goubault, Jérémy Ledent, and Sergio Rajsbaum

Information and Computation, 2021

Abstract Bibtex URL PDF

(This is the journal version of our GandALF18 paper.)
The usual epistemic model for a multi-agent system is based on a Kripke frame, which is a graph whose edges are labeled with agents that do not distinguish between two states. We propose to uncover the higher-dimensional information implicit in this structure, by introducing a topological notion of epistemic model based on simplicial complexes. We then use Dynamic Epistemic Logic to study how a simplicial model changes after a set of agents communicate with each other. We thus provide a bridge between DEL and the topological theory of distributed computability, which studies task solvability in a shared memory or message passing architecture.
```
@article{GoubaultLR21simplicial,
  author    = {{\'{E}}ric Goubault and
               J{\'{e}}r{\'{e}}my Ledent and
               Sergio Rajsbaum},
  title = {A Simplicial Complex Model for Dynamic Epistemic Logic to study Distributed Task Computability},
  journal   = {Information and Computation},
  volume    = {278},
  pages     = {104597},
  year      = {2021},
  issn = {0890-5401},
  doi       = {10.1016/j.ic.2020.104597},
}
```
Semantics,
λ-calculus
A Quantitative Model for Simply Typed λ-calculus

Martin Hofmann, and Jérémy Ledent

Mathematical Structures in Computer Science, 2021

Abstract Bibtex URL PDF

We use a simplified version of the framework of resource monoids, introduced by Dal Lago and Hofmann, to interpret simply typed λ-calculus with constants zero and successor. We then use this model to prove a simple quantitative result about bounding the size of the normal form of λ-terms. To our knowledge, our proof is the first semantic proof of this result. Our use of resource monoids differs from the other instances found in the literature, in that it measures the size of λ-terms rather than time complexity.
```
@article{HofmannL21quantitative,
  author    = {Martin Hofmann and
               J{\'e}r{\'e}my Ledent},
  title     = {A Quantitative Model for Simply Typed λ-calculus},
  journal={Mathematical Structures in Computer Science},
  publisher={Cambridge University Press},
  year      = {2021},
  pages={1–17},
  doi = {10.1017/S0960129521000256},
}
```

2020

Concurrency,
Epistemic logic
Two-agent Approximate Agreement from an Epistemic Logic perspective

Jorge Armenta-Segura, Jérémy Ledent, and Sergio Rajsbaum

In 13th Latin American Workshop on Logic/Languages, Algorithms and New Methods of Reasoning, LANMR 2020

Abstract Bibtex URL PDF

We investigate the two-agent approximate agreement problem in a dynamic network in which topology may change unpredictably, and where consensus is not solvable. It is known that the number of rounds necessary and sufficient to guarantee that the two agents output values 1/k³ away from each other is k. We distil ideas from previous papers to provide a self-contained, elementary introduction, that explains this result from the epistemic logic perspective.
```
@inproceedings{ArmentaLR20approximate,
  author    = {Jorge Armenta-Segura and
               J{\'e}r{\'e}my Ledent and
               Sergio Rajsbaum},
  title     = {Two-agent Approximate Agreement from an Epistemic Logic perspective},
  booktitle = {13th Latin American Workshop on Logic/Languages, Algorithms and New Methods of Reasoning, {LANMR} 2020},
  year      = {2020},
}
```
Category Theory,
Open Games
Compositional Game Theory, compositionally

Robert Atkey, Bruno Gavranović, Neil Ghani, Clemens Kupke, Jérémy Ledent, and Fredrik Nordvall Forsberg

In 3rd international Applied Category Theory Conference, ACT 2020

Abstract Bibtex PDF Slides

We present a new compositional approach to Compositional Game Theory based upon the notion of arrows, a concept originally from functional programming. We model equilibria as a module over an arrow and define an operator to build a new arrow from such a module over an existing arrow. We also model strategies as graded arrows and define an operator which builds a new arrow by taking the colimit of a graded arrow. We use this compositional approach to CGT to show how known and previously unknown variants of open games can be proven to form symmetric monoidal categories.
```
@inproceedings{AtkeyGGKLN20compositional,
  author    = {Robert Atkey and
               Bruno Gavranovi{\'c} and
               Neil Ghani and
               Clemens Kupke and
               J{\'e}r{\'e}my Ledent and
               Fredrik Nordvall Forsberg},
  title     = {Compositional Game Theory, compositionally},
  booktitle = {3rd international Applied Category Theory Conference, {ACT} 2020},
  year      = {2020},
}
```

2019

Concurrency,
Topology
A Sound Foundation for the Topological Approach to Task Solvability

Jérémy Ledent, and Samuel Mimram

In 30th International Conference on Concurrency Theory, CONCUR 2019

Abstract Bibtex URL PDF Slides

The area of fault-tolerant distributed computability is concerned with the solvability of decision tasks in various computational models where the processes might crash. A very successful approach to prove impossibility results in this context is that of combinatorial topology, started by Herlihy and Shavit in 1999. However, their so-called Asynchronous Computability Theorem was only proved in the context of processes communicating through read-write registers. In this paper, we prove a generalization of this theorem that applies to any kind of shared object.
```
@inproceedings{LedentM19foundation,
  author    = {J{\'{e}}r{\'{e}}my Ledent and
               Samuel Mimram},
  title     = {A Sound Foundation for the Topological Approach to Task Solvability},
  booktitle = {30th International Conference on Concurrency Theory, {CONCUR} 2019},
  pages     = {34:1–34:15},
  year      = {2019},
  doi       = {10.4230/LIPIcs.CONCUR.2019.34},
}
```
Concurrency,
Epistemic logic
A Dynamic Epistemic Logic Analysis of the Equality Negation Task

Éric Goubault, Marijana Lazić, Jérémy Ledent, and Sergio Rajsbaum

In Dynamic Logic. New Trends and Applications - Second International Workshop, DaLí 2019

Abstract Bibtex URL PDF

In this paper we study the solvability of the equality negation task in a simple wait-free model where processes communicate by reading and writing shared variables or exchanging messages. In this task, two processes start with a private input value in the set {0, 1, 2}, and after communicating, each one must decide a binary output value, so that the outputs of the processes are the same if and only if the input values of the processes are different. This task is already known to be unsolvable; our goal here is to prove this result using the Dynamic Epistemic Logic approach introduced in a previous paper. We show that in fact, there is no epistemic logic formula that explains why the task is unsolvable. We fix this issue by extending the language of our DEL framework using so-called DEL with factual change.
```
@inproceedings{GoubaultLLR19dynamic,
  author    = {{\'{E}}ric Goubault and
               Marijana Lazi\'{c} and
               J{\'{e}}r{\'{e}}my Ledent and
               Sergio Rajsbaum},
  title     = {A Dynamic Epistemic Logic Analysis of the Equality Negation Task},
  booktitle = {Dynamic Logic. New Trends and Applications - Second International Workshop, DaL{\'{i}} 2019},
  pages     = {53–70},
  year      = {2019},
  doi       = {10.1007/978-3-030-38808-9\_4},
}
```
Concurrency,
Topology
Wait-Free Solvability of Equality Negation Tasks

Éric Goubault, Marijana Lazić, Jérémy Ledent, and Sergio Rajsbaum

In 33rd International Symposium on Distributed Computing, DISC 2019

Abstract Bibtex URL PDF Slides

We introduce a family of tasks for n processes, as a generalization of the two-process equality negation task of Lo and Hadzilacos. We study the solvability of these tasks using techniques from combinatorial topology.
```
@inproceedings{GoubaultLLR19waitfree,
  author    = {{\'{E}}ric Goubault and
               Marijana Lazi\'{c} and
               J{\'{e}}r{\'{e}}my Ledent and
               Sergio Rajsbaum},
  title     = {Wait-Free Solvability of Equality Negation Tasks},
  booktitle = {33rd International Symposium on Distributed Computing, {DISC} 2019},
  pages     = {21:1–21:16},
  year      = {2019},
  doi       = {10.4230/LIPIcs.DISC.2019.21},
}
```

2018

Concurrency,
Semantics
Concurrent Specifications Beyond Linearizability

Éric Goubault, Jérémy Ledent, and Samuel Mimram

In 22nd International Conference on Principles of Distributed Systems, OPODIS 2018

Abstract Bibtex URL PDF Slides

A very general way to specify concurrent objects is to simply give the set of all the execution traces that we consider correct for the object. In many cases, one is only interested in studying a subclass of these concurrent specifications, and more convenient tools such as linearizability can be used to describe them. In this paper, what we call a concurrent specification will be a set of execution traces that moreover satisfies a number of axioms. As we argue, these are actually the only concurrent specifications of interest. Restricting to this class of concurrent specifications allows us to derive a Galois connection theorem relating different variants of linearizability.
```
@inproceedings{GoubaultLM18specifications,
  author    = {{\'{E}}ric Goubault and
               J{\'{e}}r{\'{e}}my Ledent and
               Samuel Mimram},
  title     = {Concurrent Specifications Beyond Linearizability},
  booktitle = {22nd International Conference on Principles of Distributed Systems, {OPODIS} 2018},
  pages     = {28:1–28:16},
  year      = {2018},
  doi       = {10.4230/LIPIcs.OPODIS.2018.28},
}
```
Concurrency
Brief Announcement: On the Impossibility of Detecting Concurrency

Éric Goubault, Jérémy Ledent, and Samuel Mimram

In 32nd International Symposium on Distributed Computing, DISC 2018

Abstract Bibtex URL PDF

We identify a general principle of distributed computing: one cannot force two processes running in parallel to see each other. This principle is formally stated in the context of asynchronous processes communicating through shared objects, using trace-based semantics. We prove that it holds in a reasonable computational model, and then study the class of concurrent specifications which satisfy this property.
```
@inproceedings{GoubaultLM18brief,
  author    = {{\'{E}}ric Goubault and
               J{\'{e}}r{\'{e}}my Ledent and
               Samuel Mimram},
  title     = {Brief Announcement: On the Impossibility of Detecting Concurrency},
  booktitle = {32nd International Symposium on Distributed Computing, {DISC} 2018},
  pages     = {50:1–50:4},
  year      = {2018},
  doi       = {10.4230/LIPIcs.DISC.2018.50},
}
```
Concurrency,
Epistemic logic
A Simplicial Complex Model for Dynamic Epistemic Logic to study Distributed Task Computability

Éric Goubault, Jérémy Ledent, and Sergio Rajsbaum

In Proceedings Ninth International Symposium on Games, Automata, Logics, and Formal Verification, GandALF 2018

Abstract Bibtex URL PDF Slides

The usual epistemic model for a multi-agent system is based on a Kripke frame, which is a graph whose edges are labeled with agents that do not distinguish between two states. We propose to uncover the higher-dimensional information implicit in this structure, by introducing a topological notion of epistemic model based on simplicial complexes. We then use Dynamic Epistemic Logic to study how a simplicial model changes after a set of agents communicate with each other. We thus provide a bridge between DEL and the topological theory of distributed computability, which studies task solvability in a shared memory or message passing architecture.
```
@inproceedings{GoubaultLR18simplicial,
  author    = {{\'{E}}ric Goubault and
               J{\'{e}}r{\'{e}}my Ledent and
               Sergio Rajsbaum},
  title     = {A Simplicial Complex Model for Dynamic Epistemic Logic to study Distributed Task Computability},
  booktitle = {Proceedings Ninth International Symposium on Games, Automata, Logics, and Formal Verification, GandALF 2018},
  pages     = {73–87},
  year      = {2018},
  doi       = {10.4204/EPTCS.277.6},
}
```

2017

Category Theory,
Semantics
A cartesian-closed category for higher-order model checking

Martin Hofmann, and Jérémy Ledent

In 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017

Abstract Bibtex URL PDF Slides

In previous work, the construction of an abstract lattice from a given Büchi automaton is described. This abstract lattice is finite and allows one to decide whether finite and infinite traces of first-order recursive boolean programs are accepted by the automaton. In this paper, we show how to derive from the abstract lattice a cartesian-closed category with fixpoint operator in such a way that the interpretation of a higher-order recursive program yields precisely the abstraction of its set of finite and infinite traces. Thus, this provides a new algorithm for the higher-order model checking problem for trace properties, by simply evaluating the semantics of a program in our model.
```
@inproceedings{HofmannL17ho,
  author    = {Martin Hofmann and
               J{\'{e}}r{\'{e}}my Ledent},
  title     = {A cartesian-closed category for higher-order model checking},
  booktitle = {32nd Annual {ACM/IEEE} Symposium on Logic in Computer Science, {LICS} 2017},
  pages     = {1–12},
  year      = {2017},
  doi       = {10.1109/LICS.2017.8005120},
}
```

Ph.D. Thesis

I did my PhD at École Polytechnique, supervised by Éric Goubault and Samuel Mimram.

Geometric Semantics for Asynchronous Computability

École Polytechnique, Palaiseau, France, 2019

Jérémy Ledent

PDF Slides