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Deterministic two-way transducers capture the class of regular functions. The efficiency of composing two-way transducers has a direct implication in algorithmic problems related to synthesis, where transformation specifications are converted into equivalent transducers. These specifications are presented in a modular way, and composing the resultant machines simulates the full specification.
In this talk, I will present how we can achieve efficient composition of two-way transducers, mainly through the use of Reversible Transducers. Reversible machines are machine that are both deterministic and codeterministic.
I will show how any two-way transducers can be made reversible, while being easily composable. I will also show how these results can be extended to the setting of infinite words, which is the dedicated setting for model-checking for example.

Conformance checking techniques asses the suitability of a process model in representing an underlying process, observed through a collection of real executions. An important problem for conformance checking is to align a log trace with a model, that is, to find the minimal changes necessary to correct a new observation to conform to a process model.

The subject of this work is to study conformance checking for timed models, that is, process models that consider both the sequence of events in a process as well as the timestamps at which each event is recorded. We set our problem of timed alignment and solve two cases, each corresponding to a different metric over timed traces.

Polyregular functions are the class of string-to-string functions definable by pebble transducers, an extension of finite-state automata with outputs and multiple two-way reading heads (pebbles) with a stack discipline. If a polyregular function can be computed with k pebbles, then its output length is bounded by a polynomial of degree k in the input length. But Bojańczyk has shown that the converse fails.
In this talk, I will sketch an easier proof of a stronger statement: for every k, there exists some polyregular function with quadratic growth whose output language differs from that of any k-fold composition of macro tree transducers, i.e. of any safe order-k tree transducer, and which therefore cannot be computed by a k-pebble transducer. Actually there is no need to know what these tree transducers are: the proof uses as a black box a powerful “bridge theorem” of Engelfriet and Maneth.
In fact, the proof of the bridge theorem implicitly uses a linearity argument, in the sense of linear logic. If time allows, I will briefly mention some ongoing work with Paweł Parys to extend this theorem to unsafe higher-order transducers, using a variant of the Taylor expansion of λ-terms and semi-quantitative coherence spaces.
Joint work with Sandra Kiefer and Cécilia Pradic: https://arxiv.org/abs/2301.09234

Adhesive categories are categories with structures that allows for some key results of graph rewriting theory to hold. There are also some weaker variations of this concept: rm-adhesive and rm-quasiadhesive categories.
I will present a formalization in Coq of the hierarchy of adhesive categories. This formalization relies on the Hierarchy Builder tool from the MathComp library. It is modular, with adhesive categories being at the top of a hierarchy which contains the weaker variants of adhesive categories and starts at the level of categories. Each level is equipped with several equivalent interfaces to define instances. It comes with a library of lemmas about more basic categorical concepts, such as pullbacks and regular monomorphisms.
This is my current work as a PhD student, supervised by Russ Harmer and Damien Pous.
The code can be found on this GitLab repository: https://gitlab.com/SamuelArsac/graph-rewriting

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Comment reconnaître et connaître les plantes en 2024 ? Dans cet exposé nous nous interrogerons sur la manière dont l’informatique peut servir à construire des outils conviviaux – ou non – pour identifier les plantes. Nous présenterons l’exemple de Botascopia, un outil permettant de construire des clés de détermination adaptées à une flore locale et à destination du grand public. Nous détaillerons en particulier comment les descriptions morphologiques des plantes, issues des connaissances botaniques, peuvent être représentées et manipulées par un algorithme et un langage de programmation probabiliste dédié, permettant la construction d’un logiciel modulable et explicable.

On the one side, the formalism of Global Transformations comes with the claim of capturing any transformation of space that is local, synchronous and deterministic. The claim has been proven for different classes of models such as mesh refinements from computer graphics, Lindenmayer systems from morphogenesis modeling, and cellular automata from biological, physical and parallel computation modeling. The Global Transformation formalism achieves this by using category theory for its genericity, and more precisely the notion of Kan extension to determine the global behaviors based on the local ones. On the other side, Causal Graph Dynamics describe the transformation of port graphs in a synchronous and deterministic way.

In this work, we show the precise sense in which the claim of Global Transformations holds for them as well. This is done by showing different ways in which they can be expressed as Kan extensions, each of them highlighting different features of Causal Graph Dynamics. Along the way, this work uncovers the interesting class of Monotonic Causal Graph Dynamics and their universality among General Causal Graph Dynamics.