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## Computational Complexity I

• Teacher(s):
• Course given in: English
• ECTS Credits:
• Schedule: Autumn Semester 2020-2021, 2.0h. course (weekly average)
WARNING :   this is an old version of the syllabus, old versions contain   OBSOLETE   data.
• sessions
• course website
• Related programmes:

### Objectives

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

### Contents

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.

### References

- 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"

none.

### Evaluation

#### First attempt

Exam:
Without exam (cf. terms)
Evaluation:

- 30' oral exam organized during the semester.

#### Retake

Exam:
Oral 0h30 minutes
Documentation:
Allowed with restrictions
Calculator:
Allowed with restrictions
Evaluation:

- 30' oral exam