# Coursebooks

## Computational complexity

English

#### Remark

(pas donné en 2020-21)

#### Summary

In computational complexity we study the computational resources needed to solve problems and understand the relation between different types of computation. This course advances the students knowledge of computational complexity, and develop an understanding of fundamental open questions.

#### Content

• Complexity classes (time, space, nondeterminism)
• Boolean circuits and nonuniform computation
• Role of randomness in computation (extractors, pseudo-random generators)
• Interactive proofs and zero knowledge proofs
• Probabilistically checkable proofs and their characterization of the complexity class NP (PCP Theorem)
• Communication complexity

#### Keywords

theoretical computer science

computational complexity

#### Learning Prerequisites

##### Recommended courses

Theory of computation (CS-251)

Algorithms (CS-250)

#### Learning Outcomes

By the end of the course, the student must be able to:
• Demonstrate an understanding of computational complexity and the P vs NP problem
• Formalize and analyze abstractions of complex scenarios/problems
• Express a good understanding of different concepts of proofs
• Prove statements that are similar to those taught in the course
• Use and understand the role of randomness in computation
• Illustrate a basic understanding of probabilistically checkable proofs and their characterization of the class NP (the PCP-Theorem)
• Explain recent exciting developments in theoretical computer science
• Compare different models of computation

#### Transversal skills

• Demonstrate the capacity for critical thinking
• Summarize an article or a technical report.

#### Teaching methods

Lecturing and exercises

#### Expected student activities

Actively attending lectures and exercise sessions.  Also homeworks and exam.

#### Supervision

 Office hours Yes Assistants Yes Forum Yes

#### Resources

No

##### Bibliography

Sanjeev Arora and Boaz Barak: Computational Complexity: A Modern Approach, Cambridge University Press.

### Reference week

MoTuWeThFr
8-9
9-10   INR113
10-11INM10
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22

Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German