updated README

README.md

@@ -1,7 +1,52 @@
-Information link:
+What is DEES and what does it do?
+
+DEES is a is a _Multiplicity Automata_ (MA) inference algorithm.
+This C++ program is about 7,500 lines (10,000 with comments).
+The theory behind this algorithm can be found in the following papers:
+
+- [Learning rational stochastic languages (COLT 2006)](http://yann.esposito.free.fr/pub/colt2006.pdf)
+
+A Multiplicity Automaton can be seen as a generalisation of Hidden Markov Models (HMM). See this [paper for more details](http://yann.esposito.free.fr/pub/Links_PA_HMM.pdf).
+
+So mainly DEES is an algorithm that learn both the parameters and the structure of HMM.
+And for that it doesn't use an euristic but properties proven to converge.
+In fact DEES can generate HMM but also more generic models.
+These models are the Multiplicity Automata (mainly, imagine an HMM with some parameter being able to be negative).
+
+It takes a sample of many sequences (or words) generated by a target probability distribution and return a model (a multiplicity automaton) generating a probability distribution as close as possible of the target distribution.
+
+We can restric the learned model to be:
+
+- a Multiplicity Automaton
+- a Probabilistic Automaton (PA) (another name for Hidden Markov Models - HMM) ; in this case the identified class is the set of Probabilistic Residual Automata (PRA)
+- a Probabilistic Deterministic Automaton (PDA)
+
+## Features
+
+The main features of DEES are:
+
+- Multiplicity automata (MA) inference from a sample of sequences.
+- Probabilistic Automata (PA) Inference
+- Probabilistic Deterministic Automata (PDA) Inference
+
+This repository also contains many other features:
+
+- Viterbi algorithm
+- Baulm-Welch algorithm
+- Random generation methods of MA, PA, PRA and PDA
+- GraphViz export of models
+- Sample generation from an MA
+- Model class detection (MA, PA, PRA, PDA)
+- Compute, if it exists, the sum of all values of all the words of a distribution generated by a MA.
+- Convertion between Alergia, MDI and DEES file format ; sample and automata
+- Generation of the trimmed MA of an MA in linear time
+- If GraphViz is intalled, model are shown and export them in PDF
+
+## More informations
 
 http://yann.esposito.free.fr/dees.php?css=blue.css&lang=en
 
-For more information you can read my [Ph.D. thesis](http://yann.esposito.free.fr/pub/these.pdf).
+If you want all the gory details you can check my [Ph.D. thesis](http://yann.esposito.free.fr/pub/these.pdf) written in French.
 
-Contact me for any question. I'll be happy to talk to you.
+Contact me if you have question.
+I'll be happy to talk to you.