Jobs/M2 AD 2014 minimisation-automates

	Minimization of automata
Reference id	M2 AD 2014 minimisation-automates
Dates	5 - 6 months in 2014
Research field	Automata Theory
Related project	Vaucanson
Advisor	Akim Demaille
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 (eg rational expressions). Vaucanson 2 is a project with financial aid from ANR (National Resaearch Agency) developed in partnership between Telecom ParisTech (Jacques Sakarovitch), LaBRI (Sylvain Lombardy) and the LRDE (Alexandre Duret-Lutz and Akim Demaille). 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.
Prerequisites
Objectives	The minimization of an automaton consists of its "optimization": it means building the smallest equivalent automaton. There are many algorithms for the minimization of automata, whose fields of application and performance vary. The task of the intern will be to implement some of these algorithms in Vaucanson 2, to optimize them, and to conduct a comparative study of their performance. These results will provide an adaptive approach that selects the algorithm to be applied depending on the profile of the automaton / transducer.
Benefit for the candidate
References	Some references Jacques Sakarovitch, “Elements of Automata Theory,” Cambridge University Press. Akim Demaille, Alexandre Duret-Lutz, Sylvain Lombardy, Jacques Sakarovitch. “Implementation Concepts in Vaucanson 2,” CIAA’13. Jean Berstel, Luc Boasson, Olivier Carton, Isabelle Fagnot, “Minimization of automata.” Marie-Pierre Béal, Maxime Crochemore, “Minimizing incomplete automata.”
Place	LRDE: How to get to us
Compensation	800€ euros gross/month
Future work opportunities	If you have performed the internship satisfactorily, we would like it to be followed by a PhD thesis.
Contact	<akim . demaille at lrde . epita . fr> <akim . demaille at lrde . epita . fr>