Within SINF1BA : LSINF1101

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

- 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 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”.*

- 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

- lectures
- exercises supervised by a teaching assistant

- written exam (September, oral exam)

Background:

- SINF1121 Advanced algorithmics and data structures

- 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**