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.
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 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 Notes Lecture I
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
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