Jobs/M2 AD 2015 Symmetric Difference Automata
|Symmetric Difference Automata|
M2 AD 2015 Symmetric Difference Automata
5-6 months in 2015
|General presentation of the field||
The classical theory of automata, of transducers and of rational expressions, admits a very elegant and extremely useful extension (eg, in natural language processing) taking into account the concept of weighting. The weights are then taken in a semi-ring, which can be classical (⟨𝔹, ∨, ∧⟩, ⟨ℤ, +, ×⟩, ⟨ℚ, +, ×⟩, etc..), tropical (⟨ℤ, min, +⟩, etc..), or yet of another type (e.g. rational expressions).
The field 𝔽₂ is a particular interest, and shows quite a few unique properties, as demonstrated by the current active research under various names (e.g., "Symmetric Difference Automata").
Vcsn is a project led by Alexandre Duret-Lutz and Akim Demaille (LRDE). It is a platform for the manipulation of automata, transducers and weighted rational expressions. It is written in C++11 avoiding the classical object-oriented programming in favor of generic programming (template) for more performance. Vcsn is an heir of the Vaucanson 2 project which was developed in partnership with Jacques Sakarovitch (Telecom ParisTech) and Sylvain Lombardy (LaBRI).
The objective of this internship is to exploit the existing features of Vcsn to apply them to 𝔽₂ in a first step, and then, in a second step, to use Vcsn as a tool to explore novel results.
|Benefit for the candidate|
|Place||LRDE: How to get to us|
1000 € gross/month
|Future work opportunities||
If you have performed the internship satisfactorily, we would like it to be followed by a PhD thesis.