Algorithmics and computability

Duration

30h Th, 20h Pr

Number of credits

Lecturer

Emilie Charlier

Language(s) of instruction

French language

Organisation and examination

Teaching in the first semester, review in January

Schedule

Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

This lecture deals with this fundamental question : what kind of problem (being admitted that it can be coded into a computer) can be solved by a computer program ?
To be able to answer this question, we first have to give a formal definition of the notions of algorithm and of computable function. This is done through the use of Turing machine. The main topics are : primitive recursive functions, recursive functions, computable functions, Turing machines, universal Turing machine, Church-Turing's thesis, decidable problem, the halting problem, decidable and acceptable languages, Cook's theorem, complexity theory, NP-completeness, ...
The lecture ends with the presentation of some well-known NP-complete problems (in optimization or graph theory for instance) like the travel salesman problem.

Learning outcomes of the learning unit

At the end of this course, the student will master fundamental notions arising in computability and complexity theory as well as the corresponding proofs. In particular, the student will integrate the concepts of computable functions and decision problem. He/she will be able to explain, using convenient reductions, that some problems do not have any algorithmic solution. Also he/she will be able to build some Turing machines and prove NP-completeness of classical problems.

Prerequisite knowledge and skills

No specific programming skill is needed.

Planned learning activities and teaching methods

Theoretical lectures using "blackboard and chalk" interacting with students. During exercises sessions, students are facing exercises that must be solved.

Mode of delivery (face to face, distance learning, hybrid learning)

The theoretical part of the course is dedicated to theoretical aspects of Turing machines and complexity theory. Practical sessions are devoted to solve exercises and to enlighten the concepts presented during the lecture.
If the number of students is greater than or equal to 5, lectures will be given with a board and chalk, in interaction with the students. Otherwise, the organizational arrangements will be discussed at the first course.
 

Organisational adjustments related to the current health context

Recommended or required readings

The course will be based on the lecture notes of P. Lecomte and of M. Rigo. Both are in French and are available online at www.discmath.ulg.ac.be/charlier. They also can be printed from the Mathematics Department office.
Some textbooks:

• R. Cori, D. Lascar, Logique Mathématique, Dunod (1993).
• M. R. Garey, D. S. Johnson, Computers and Intractability, A guide to the Theory of NP-Completeness, W. H. Freeman and Company, (1979).
• H. R. Lewis, C. Papadimitriou, Elements of the Theory of Computation, Prentice-Hall, (1981).
• A. Turing, On Computable Numbers, with an Application to the Entscheidungsproblem, Proc. London Math. Society. Second Series 42, 230-265, (1936).
• P. Wolper, Introduction à la calculabilité, Dunod (2006).

Assessment methods and criteria

Below you will find information on the evaluation methods planned for in-person and remote exams as well as those planned for hybrid sessions. Depending on how the health crisis evolves, the chosen method will be communicated to you no later than one month before the start of the exam session.

The final examination is divided into an oral part and a written exam. The oral exam is devoted to the theory but also direct applications of the theory (student may be asked to solve a small exercise on the blackboard or on a sheet of paper). The written exam evaluate the comprehension of the material of the exercice sessions.

Work placement(s)

Organizational remarks

This course is organized once every two years : 2017-2018, 2019-2020, ...
Some useful informations are given on http://www.discmath.ulg.ac.be/charlier/enseignement.html.

Contacts

Émilie Charlier - titulaire Célia Cisternino - assistante   Département de Mathématique (B37) Quartier Polytech 1 Allée de la Découverte,12 B-4000 Liège
Tél. : +32 4 366.93.84 E-mail : echarlier@uliege.ac.be ccisternino@uliege.ac.be