Within SINF1BA : LSINF1101
Within FSA1BA : LFSAB1101, LFSAB1102, LFSAB1202, LFSAB1202, LFSAB1301, LFSAB1401
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.
- 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
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 Engineering" 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”.
- written exam (September, oral exam)
- lectures
- exercises supervised by a teaching assistant
-
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
Slides online
References
- 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
Background:
- SINF1121 Advanced algorithmics and data structures
