Logic and Automata Theory

A course in the EPFL Doctoral Program in Computer and Communication Sciences

• Official Course Book Page
• the course carries 4 credits

Objectives: Many major hardware (Intel, IBM) and software (Microsoft) companies are now using the technique of Model Checking in practice. Examples of its use include the verification of VLSI circuits, communication protocols, software device drivers, real-time embedded systems, and security algorithms. The works of A. Pnueli, E. Clarke, E.A Emerson and J. Sifakis on algorithmic verification of systems using the Model Checking has been awarded the 1996 and 2007 Turing awards. The basis of this work is the relation of logic with automata theory, which was introduced by the seminal works of Buechi (1960) and Rabin (1969). This course is intended to introduce the student to these techniques, focusing on decision methods for classical non-interpreted logics and integer arithmetic theories.

Syllabus:

1. Classical first- and second-order logic, finite word and tree automata, closure properties and language emptiness.
2. Relationship between Weak Monadic Second-Order Logic and finite automata. Infinite automata on words (Buechi, Mueller) and on trees (Rabin) automata, and their relationship with Monadic Second-Order Logic.
3. Game theory. Proof of Rabin's Complementation Theorem. Application of game theory to Mu-calculus, a widely used tool for specification and verification of systems.
4. Logical theory of integer arithmetic. Decidability results using both quantifier elimination and automata theory. Cobham's base dependence theorem.

Schedule: (lectures and exercises): Fridays 13:15-16:00

First lecture: 18.9.2009
Last lecture: 18.12.2009

Location: BC 355

Instructors:

• Radu Iosif
• Barbara Jobstmann

Organized by: Viktor Kuncak

Preliminary Outline:

1. 18.09.2009 Introduction
2. 25.09.2009 First Order and Monadic Second Order Logicsslide1.pdf (Radu Iosif)
3. 02.10.2009 Automata on finite wordsslide2.pdf (Radu Iosif)
4. 09.10.2009 Automata on infinite wordsslide3.pdf (Radu Iosif)
5. 16.10.2009 Linear Temporal Logicltl-slide.pdf (Radu Iosif)
6. 23.10.2009 Automata on finite treesslide4.pdf (Radu Iosif)
7. 30.10.2009 Automata on infinite treesslide5.pdf (Radu Iosif)
8. 06.11.2009 Games: Terminology, Reachability, Safety, and Buchi games slide6.pdf (Barbara Jobstmann)
9. 13.11.2009 MC and Repair Example slide7.pdf, Obligation and Weak-Parity games slide8.pdf (Barbara Jobstmann)
10. 20.11.2009 Parity games slide9.pdf (Barbara Jobstmann)
11. 27.11.2009 Muller Games, Relation between games and tree automata slide10.pdf (Barbara Jobstmann)
12. 04.12.2009 Integer Arithmetic, Presburger Arithmetic and Semilinear Sets presburger-slide.pdf (Radu Iosif)
13. 11.12.2009 Definability and Recognizability of integer sets recognizable-slide.pdf (Radu Iosif)
14. 18.12.2009 End-of-Term In-Class Quiz

Homework

Please find the homework here.

Bibliography

• W. Thomas. Handbook of Theoretical Computer Science, Volume B, Chapter 4. Automata on Infinite Objects
• B. Khoussainov and A. Nerode. Automata Theory and its Applications ISBN 0-8176-4207-2
• Tree Automata Techniques and Applications Collective Online Book
• M. Vardi. The Buchi Complementation Saga. stacs07.pdf
• S. Schewe. Büchi complementation made tight. STACS 2009
• A genealogy of LTL to Buechi automata translations http://spot.lip6.fr/wiki/LtlTranslationAlgorithms
• A genealogy of Buechi emptiness checking algorithms http://spot.lip6.fr/wiki/EmptinessCheckAlgorithms
• V. Bruyere, G. Hansel, C. Michaux and R. Villemairez. LOGIC AND p-RECOGNIZABLE SETS OF INTEGERS. bru.pdf

Software

• The Mona Project : http://www.brics.dk/mona/
• The Goal Project : http://goal.im.ntu.edu.tw/wiki/doku.php
• The Gastex Package for Latex : http://www.lsv.ens-cachan.fr/~gastin/gastex/gastex.html

Related Lectures

• Software Analysis and Verification (SAV 2009), Lecture 1
• Software Analysis and Verification (SAV 2009), Lecture 10
• Dejan Nickovic. Aperiodic Languages star-free-pres.pdf

More details will follow. The course will be similar to the following course.