# Computability and complexity

LINGI1123  2018-2019  Louvain-la-Neuve

Computability and complexity
5.0 credits
30.0 h + 30.0 h
2q

Teacher(s)
Deville Yves ;
Language
Français
Prerequisites

Within SINF1BA : LSINF1101

Within FSA1BA : LFSAB1101, LFSAB1102, LFSAB1202, LFSAB1202, LFSAB1301, LFSAB1401

Main themes
• Computability : problems and algorithms, computable and non computable functions, reductions, undecidable classes of problems (Rice), fix point theorem, Church-Turing thesis
•  Main computability models : Turing machines, recursive functions, lambda calculus, automates
• Complexity theory : complexity classes, NP-completeness, Cook's theorem, how to solve NP-complete problems
Aims

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 completing successfully this course will be able to

• recognize, explain and identify the limits of computing science ;
• explain the main computability models especially  their foundations, their similarities and their differences
• identify, recognize and describe non computable and untractable problems

Students will have developed skills and operational methodology. In particular, they have developed their ability to

• have a critical look at the performance and capabilities of computer systems

The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.

Content
• Introduction
• Concepts: demonstration and reasoning, sets, Cantor's diagonalization
• Computability: basic results
• Models of computability
• Analysis of the Church-Turing thesis
• Introduction to computational complexity
• Complexity classes and NP completeness
Teaching methods
• lectures
• exercises supervised by a teaching assistant
Evaluation methods
• written exam (September, oral exam)
Other information

Background:

• SINF1121 Advanced algorithmics and data structures
Online resources
Bibliography
• Transparents en ligne
• Syllabus collaboratif

Livres de référence

• O. Ridoux, G. Lesventes.  Calculateurs, calculs, calculabilité. Dunod  Collection Sciences Sup, 224 pages, 2008.
• P. Wolper Introduction à la calculabilité 2nd Edition, Dunod, 2001.
• Sipser M. Introduction to the Theory of Computation PWS Publishing Company, 1997
Faculty or entity

#### Programmes / formations proposant cette unité d'enseignement (UE)

Program title
Sigle
Credits
Prerequisites
Aims
Master [120] in Mathematical Engineering
5
-

Minor in Engineering Sciences: Computer Sciences