Tito's presence on the Web

Welcome to my homepage! I am a researcher in theoretical computer science at École normale supérieure de Lyon, Plume team, on an individual postdoctoral fellowship from LabEx Milyon. (And here’s my submitted research project in French. Warning: some of the stuff on infinite alphabets turns out not to work.)

Previous positions (click-to-expand using the HTML5 <details> element)

Contact / personal information

Family name: Nguyễn
Given name: Lê Thành Dũng
E-mail address: nltd at nguyentito dot eu
Social media: @tito@types.pl (Mastodon) | CS Theory StackExchange | ORCID
Visual identification: photo (taken by Lwenn Bussière-Caraes)

Actually important stuff

The overriding concern of our age is the ongoing environmental disaster. There is a Pledge for sustainable research in theoretical computer science that you can sign if you work in that field, and one of its creators, my colleague Antoine Amarilli, has a lovely list of actions and commitments that he takes out of concern for the climate crisis; personally, I am a vegetarian and I haven’t boarded a plane since summer 2019 (from personal experience, Praha→Paris and Lyon→Wrocław→Warszawa→Leipzig are completely doable by some combination of train and night bus). The issues raised by the Just Mathematics Collective – social justice and the ethical implications of our work – are also of the utmost importance.

I’m glad to see that virtual conferences have taken off (out of necessity), but worried by the widespread use of tools with serious privacy and security issues. As computer scientists, we should hold ourselves to a higher standard so that society at large can follow our example! (Update around 2 years after writing this: the reign of Zoom shows no signs of stopping, sadly.)

All my publications until now are open access. I refuse to submit my work to any venue that does not meet this requirement (being allowed to upload a preprint is not sufficient), no matter how prestigious it may be – anyway, publications should be judged on their own merits. (I’ve been pressured to do so before, and was relieved that the paper was rejected.) I also pledge not to provide peer review for closed-access venues.

At one point, my intention was not to apply for permanent academic positions after my PhD, in order to escape the distorted incentives of contemporary research and the countless annoyances that well-meaning people will put you through for the sake of “career optimization”. Nowadays, I’m open to somehow landing such a position if it does not involve compromising on the above points nor spending actual effort on specifically compensating for this rigid stance. If you’re a non-tenured researcher intending to stay in academia, following my example may or may not be career suicide (corollary: you should probably not collaborate with me, which is pretty sad, but blame the system; though I probably have a less toxic attitude towards meeting deadlines than other colleagues).


My research used to focus on connections between linear logic, a logical system born out of the proofs-as-programs correspondence (“Curry-Howard isomorphism”), and other topics in theoretical computer science such as graph theory, computational complexity, formal languages… Nowadays I also invest much of my working time in this latter field — more precisely, finite automata / transducers / semigroups. I also enjoy categorical perspectives and approaches to all of the above; those are well-established applications of category theory, but not the trendy kind of “applied category theory”.

Outside of my research, I also have other scientific interests which I lack the time to pursue:

I tend to agree with David Madore when he says that “the only people interested in publication lists look like they to want to count them, not to read them” (translation mine). Nevertheless, if you’re looking for a specific paper of mine, it should be hyperlinked in the middle of some relevant explanatory paragraph below. (For bean-counting purposes my dblp profile is not too hard to find, though it has a missing tilde on my family name – this spelling issue also occurs on arXiv due to lack of Unicode support.)

Expository and/or not my own work

A note on arXiv about a simple theorem in discrete geometry / linear algebra. (To be updated with a much simpler proof by Dorian Nogneng.)

Some slides on the expressivity of the simply-typed λ-calculus:

Implicit automata in typed λ-calculi

Implicit computational complexity seeks to characterize complexity classes by using constrained programming languages. Pierre Pradic and I have been exploring a counterpart for automata and transducers, relying on subsystems of linear logic. This has also led us to revisit automata-theoretic construtions in a categorical framework. I’ve been surprised and elated to see that our work has even been mentioned in a talk by Gordon Plotkin!

See my PhD dissertation, titled Implicit automata in linear logic and categorical transducer theory, and the slides of the defense (in French); or Pierre’s website for more papers on the topic. In an upcoming single-authored paper, currently in preparation, I solve Conjecture 1.4.3 of my dissertation on the “non-uniformly definable functions” in the simply typed λ-calculus; this has been the subject of blackboard talks in seminars.



One byproduct of the research carried out in my PhD has been to investigate automata models that compute string-to-string functions. Pradic and I have proved a few things about such devices (called transducers), some of which are unpublished; see the slides below. One of these unpublished results is a collaboration with Sandra Kiefer. I have also been fortunate to interact with several talented researchers (such as Mikołaj Bojańczyk, Gaëtan Douéneau-Tabot and Nathan Lhote) on the subject of polyregular functions.


Denotational semantics of polymorphism vs space complexity

What led me to automata (cf. above) was finding out that regular languages occur in a language with linear types designed for implicit complexity. It turns out that the proof for this relies on old ideas on the denotational semantics of second-order linear logic. Another direction was to understand how to go beyond regular languages using the same ideas.

The result was an implicit characterization of logarithmic space, whose proof uses a bit of semantics and of category theory (in particular normal functors). The implicit complexity side of the story – a joint work with Pierre Pradic – was published. The semantics side is far from being as rigorous as I would like and is projected to be rewritten after I finish my PhD thesis; in the meantime, you can take a look at this old preprint. Here is a talk targeted at a broad audience, that does not require prior knowledge of linear logic.

Some further material on the semantics of second-order logic can be found in in an obsolete preprint (joint work with Paolo Pistone, Thomas Seiller and Lorenzo Tortora de Falco). The Chocola talk slides below also contain some ideas that I haven’t pursued further for now.

Talks (for an audience familiar with linear logic and/or denotational semantics)
Talks (for the implicit computational complexity community)

Combinatorics of proof nets

In a pioneering work whose significance has been underestimated in my opinion, Christian Retoré provided a translation from proof nets for linear logic, a graphical representation of proofs, to graphs equipped with perfect matchings. This relates the combinatorially tricky theory of proof nets with a well-studied counterpart in mainstream graph theory. I strengthened and refined the correspondence between the two – the relationship is not bijective, but it turns out there are reductions in both directions preserving many structural properties – and derived a lot of consequences that had been overlooked. See my journal paper extending the work I presented at the FSCD 2018 conference (cf. list of talks).

More recently, Lutz Straßburger and I have looked at Retoré’s pomset logic (and Guglielmi’s closely related system BV, the original deep inference system) using the same tools. We hope that the significantly extended journal version of our CSL 2022 paper will serve as a useful reference for these two systems.

With Thomas Seiller, we also built a “geometry of interaction” model of linear logic which gives an interactive explanation of a correctness criterion by Retoré based on cographs. More recently, we realized that this could be extended to pomset logic (see the end of these slides).

At the end of these slides I explain why proof net correctness for cyclic MLL (a non-commutative logic) can be decided in linear time, using a criterion by Paul-André Melliès reformulated using combinatorial maps.

Finally, in another arXiv note, I prove some purely graph-theoretic minor results initially motivated by my work on proof nets. In particular, this concerns edge-colored graphs and paths/trails avoiding forbidden transitions.

Talks (for logicians)
Talks (for graph theorists)
Related: unfruitful work in combinatorial optimization (Master’s internship) In 2016, I did a 4-month internship with Christoph Dürr and Nguyễn Kim Thắng for my master’s degree. We tried to design an approximation algorithm for the online node-weighted Steiner forest problem. Our approach didn’t work, but we improved our understanding of the difficulty of the problem. However, thanks to a recreational algorithmic puzzle given by Christoph during this internship, I learned about the relationship between perfect matchings and edge-colored graphs, which would eventually lead to my above-mentioned work. You can see my first ideas on these topics and their connection to linear logic in the slides of the defense (in French).

Involvement in computer science teaching / outreach

Science popularization

In 2015, Jérémy Ledent and I wrote some articles for Tangente, a French math magazine for high schoolers, on the aforementioned proofs-as-programs correspondence and on homotopy type theory.


As a member of the Prologin organization from 2014 to 2018, I helped organize Prologin, a programming contest for people under 20 years old, and Girls Can Code!, a summer coding camp.

I was in charge of the semifinals problems in 2015 and 2016. Furthermore, in 2015, I was the main developer on the game for which the contestants had to write an AI during the finals; and from mid-2015 to mid-2016, I was heavily involved in the logistics of both Prologin and Girls Can Code! as a board member.

From 2017 to 2018, I designed and implemented programming contest exercises as a freelance consultant for Isograd, selling the skills that I had developed thanks to Prologin to the private sector.

University teaching

In the 2021-2022 I am working as a teaching assistant in Université Rennes 1. I am teaching NoSQL databases this semester, and deductive program verification in the next one.

From 2018 to 2021, I was a TA at Institut Galilée as part of my PhD, on topics such as hardware architecture, Unix system calls, algorithms and data structures, parallel random-access machines and λ-calculus, functional programming with OCaml, and XML technologies.

In 2016, I gave tutorial sessions for the Algorithms course given by Gaël Mahé at Université Paris 5 Descartes (now merged into Université de Paris) for second-year students.