Teacher(s)

Deville Yves;

Language

French

Prerequisites

This course assumes that the student acquired programming skills,
algorithmic and programming language targeted in course LEPL1402 and discrete mathematics as seen in courses LINFO1114 or LEPL1108

The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.

Main themes

• Theory of computability: problems and algorithms, computable and non-computable functions, reduction, undecidable problem classes (Rice's theorem), fixed point theorem, Church-Turing thesis
• Logic: logic of propositions and logic of predicates (syntax, semantics, proof, quantifiers, model checking, resolution)
• Computability Models: Turing Machine
• Theory of complexity: complexity classes, NP-completeness, Cook's theorem, NP-complete problem solving.

Aims

At the end of this learning unit, the student is able to :
1	Given the learning outcomes of the "Bachelor in Engineering" program, this course contributes to the development, acquisition and evaluation of the following learning outcomes: AA1.1, AA1.2 AA2.4 Given the learning outcomes of the "Bachelor in Computer science" program, this course contributes to the development, acquisition and evaluation of the following learning outcomes: S1.I3, S1.G1 S2.2 Students who have successfully completed this course will be able to recognize, explain and identify the limitations of information processing by a computer; explain and make good use of the main computability models by explaining their bases, differences and similarities; convert current language assertions into logical expressions using the syntax and semantics of the logic of propositions or predicates recognize, identify and apprehend non-calculable problems as well as intrinsically complex problems. Students will have developed methodological and operational skills. In particular, they will have developed their capacity to take a critical look at the performance and capacity of computer systems

Content

• Introduction
• Concepts : enumerable sets
• Computability: fondamenbtal results
• Models of computability
• Analysis of Church-Turing thesis
• Introduction to algorithmic complexity
• Complexity classes

Teaching methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

This course can be given in a variety of face-to-face and distance modalities.  These may include lectures, readings, preparations, exercises, as well as individual or group work.

Evaluation methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

Different modes of evaluation can be organized: continuous assessment, graded work, participation, exam.  The exam will be written, but in case of doubt on the part of the teacher as to the grade to be given to a student, the student may be questioned orally.

Faculty or entity

INFO