Computational complexity
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)
- Space complexity (Logspace, L vs NL)
- Boolean circuits and nonuniform computation
- Power of randomness
- Lower bounds for concrete models of computation: Decision trees, communication protocols, propositional proofs.
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.
Assessment methods
Three homeworks and final exam
Resources
Bibliography
Sanjeev Arora and Boaz Barak: Computational Complexity: A Modern Approach, Cambridge University Press.
Stasys Jukna: Boolean Function Complexity, Springer
Ressources en bibliothèque
Moodle Link
In the programs
- Semester: Fall
- Exam form: During the semester (winter session)
- Subject examined: Computational complexity
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: During the semester (winter session)
- Subject examined: Computational complexity
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: During the semester (winter session)
- Subject examined: Computational complexity
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: During the semester (winter session)
- Subject examined: Computational complexity
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: During the semester (winter session)
- Subject examined: Computational complexity
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: During the semester (winter session)
- Subject examined: Computational complexity
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: During the semester (winter session)
- Subject examined: Computational complexity
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: During the semester (winter session)
- Subject examined: Computational complexity
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: During the semester (winter session)
- Subject examined: Computational complexity
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: During the semester (winter session)
- Subject examined: Computational complexity
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: During the semester (winter session)
- Subject examined: Computational complexity
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: During the semester (winter session)
- Subject examined: Computational complexity
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional