Objectifs

Understanding the basic concepts of computational complexity theory and being able to recognize typical P-complete, NP-complete, PSPACE-complete problems.

Contenus

The theory of Computational Complexity focuses on classifying problems that are solvable by computers, relatively to their difficulty -- which is usually measured in how much time is needed or how much space (memory) is required. This leads on one hand to the definition of various complexity classes, and on the other hand to the comparison of computable problems by mean of reduction relations.
This course introduces to the basic concepts of computational complexity theory and gives an overview of some of the major P and NP complete problems by going through the following notions:

- Strings, languages and decision problems

- Finite automata, determinism and non-determinism√A computation model: the Turing machine

- Recursive and recursively enumerable languages and functions

- The universal Turing machine and the halting problem

- Computable and uncomputable, decidability and undecidability

- Space and time efficiency, the big-Oh notation

- Deterministic time and P

- Non-deterministic time and NP

- Reducibility and completeness

- P-complete problems such as circuit value problem, Horn clauses, linear programming, Conway's game of life

- NP-complete problems such as SAT, 3SAT, travelling salesman problem, graph coloring, Hamiltonian path problem

- LOGSPACE, PSPACE, EXPTIME, EXPSPACE.

Références

- Sanjeev Arora, Boaz Barak "Computational Complexity: A Modern Approach"

- Oded Goldreich "P, NP, and NP-Completeness: The Basics of Computational Complexity"

- Christos H. Papadimitriou "Computational Complexity"

- Michael Sipser "Introduction to the Theory of Computation"

Pré-requis

none.

Evaluation

1ère tentative

Examen:

Sans examen (cf. modalités)  

Evaluation:

- 30' oral exam organized during the semester.

- exercise participation grade

Final grade: 1/2 oral exam + 1/2 participation grade

Rattrapage

Examen:

Oral 0h30 minutes

Documentation:

Autorisée avec restrictions

Calculatrice:

Autorisée avec restrictions

Evaluation:

- 30' oral exam

- exercise participation grade

Final grade: 1/2 oral exam + 1/2 participation grade