Master Parisien de Recherche en Informatique (MPRI)


Cours 2-16 Modélisation par automates finis — 2011–2012

Plan du cours et intervenants

  1. Automates finis à multiplicité. (12h, Jacques Sakarovitch)
  2. Classification des transductions. (12h, Christian Choffrut)
  3. Groupes d'automates (6h, Inès Klimann)
  4. Automates à coûts (18h, Thomas Colcombet)
Pour la description générale du cours et ses objectifs, de même que pour la description des parties du cours autres que la mienne, se reporter à la page du cours sur le site du MPRI (liens ci-dessus).

Contôle des connaissances

Le contrôle des connaissances se fait en deux phases: un examen écrit à la fin de chacune des deux séquences et portant sur le programme vu pendant cette séquence.

Langue du cours

Le cours est donné a priori en français, mais si des étudiants non francophones le demandent, le cours aura lieu en anglais. De fait, pour l'année 2010/2011, le cours a été donné en anglais, aussi les informations qui suivent sont également rédigées en anglais.

Part 1.— Weighted Automata

• Lecture notes and references

As a background, I use my book Elements of Automata Theory (Cambridge University Press, 2009) for all references to sections and exercices below. A number of copies of this book are available for lending to students.

This book is the corrected English translation of Eléments de théorie des automates (Vuibert, 2003) where the same references are to be found as well. Some copies of this original edition are available for lending as well, but should be accompanied by the errata. The last version of the errata is to be found here.

A more recent version of a part of Chapter III of EAT has been written for Chapter 4 of the Handbook of Weighted Automata published by Springer in 2009. By special authorisation, a copy of this chapter, rewritten with the notation used in the lectures, is to be found here under the condition it will not be further distributed. The references to this text are prefixed by `HWA'.

Some lecture notes are under writing and will be made available as soon as possible.

• Plan of the lectures

The following plan is only tentative, and very optimistic. It may well be the case that not all the material described here will be treated.

The page will be updated after each lecture, in order to reflect what has really been presented.

Lecture I   —  16/09/11.     Weigted automata, a reminder?

0. Prerequisite Test
1. Weighted automata, a reminder?   EAT III.2.1, EAT III.2.3, HWA 2.2.1, HWA 3.1

• Lecture Notes   Lecture 0,

• (Highly) recommended exercises   III.2.1, III.2.2, III.2.3, III.2.10, III.2.20

• Sets of slides dealing with the topics of Lecture I
The Fundamental Theorem of Finite Automata
Recognisable series

Lecture II   —  23/09/11.   Reduction

1. The universal determinisation process.  
2. Characterisation of recognisable series.   EAT III.4.1, HWA 5.1.
3. Reduction of recognisable series.   EAT III.4.3, HWA 5.2.

• Lecture Notes   Lecture I

Exercises A   —   30/09/11.       Sheet of exercises

Lecture III   —   07/10/11.     Conjugacy and covering.

1. Morphisms of Boolean automata     EAT II.3.1
2. Local properties of morphisms     EAT II.3.2
3. A key construction: the Schützenberger covering     EAT II.3.4.
4. Conjugacy of K-automata     HWA 3.3.1., Lecture notes
5. Morphisms of K-automata     EAT III.2.5, HWA 3.3.1, HWA 3.3.2.

• Lecture Notes   Lecture II

• Set of slides dealing with the topics of Lecture III
Morphisms and coverings of Boolean automata
Morphisms of K-automata

Lecture IV   —  14/10/11.     Uniformisation.

1. Hadamard product of recognisable series     EAT III.3.2
2. The rational skimming theorem     EAT III.4.4.2
3. Kleene--Schützenberger theorem (representability theorem) for rational relations     EAT IV.1.1, EAT IV.1.5
4. Uniformisation of rational relations     EAT V.2.1, V.2.2

• Set of slides dealing with the topics of Lecture IV
Uniformisation of rational relations

Exercises B   —  21/10/11.       Sheet of exercises

Written Exam   —  02/12/11.      

Documentation

Written exam of the year 2010-2011:    French version of the exam;    English version of the exam;    French version of the solution of the exam.  
Written exam of the year 2008-2009.
Written exam of the year 2007-2008.
Written exam of the year 2006-2007.
Written exam of the year 2005-2006.


Last modification: 26 October 2011