A course is the basic teaching unit, it's design as a medium for a student to acquire comprehensive knowledge and skills indispensable in the given field. A course guarantor is responsible for the factual content of the course.
For each course, there is a department responsible for the course organisation. A person responsible for timetabling for a given department sets a time schedule of teaching and for each class, s/he assigns an instructor and/or an examiner.
Expected time consumption of the course is expressed by a course attribute extent of teaching. For example, extent = 2 +2 indicates two teaching hours of lectures and two teaching hours of seminar (lab) per week.
At the end of each semester, the course instructor has to evaluate the extent to which a student has acquired the expected knowledge and skills. The type of this evaluation is indicated by the attribute completion. So, a course can be completed by just an assessment ('pouze zápočet'), by a graded assessment ('klasifikovaný zápočet'), or by just an examination ('pouze zkouška') or by an assessment and examination ('zápočet a zkouška') .
The difficulty of a given course is evaluated by the amount of ECTS credits.
The course is in session (cf. teaching is going on) during a semester. Each course is offered either in the winter ('zimní') or summer ('letní') semester of an academic year. Exceptionally, a course might be offered in both semesters.
The subject matter of a course is described in various texts.
MI-CPX Complexity Theory Extent of teaching: 3P+1C Instructor: Completion: Z,ZK Department: 18101 Credits: 5 Semester: Z Annotation:
Students will learn about the fundamental classes of problems in the complexity theory and different models of algoritms and about implications of the theory concerning practical (un)solvability of difficult problems.
Lecture syllabus:
1. Models of computation.\r 2. Algorithmic undecidability.\r 3. Nondeterminism, the class NP, the existence of an NP-complete problem.\r 4. NP-complete problems.\r 5. Problem P=NP, relativization, classes coNP and NP intersection coNP.\r 6. The class PSPACE, Savitch theorem, hierarchy in PSPACE.\r 7. PSPACE-complete problem (quantified formulae and games), complete problem for the hierarchy classes.\r 8. Circuit and algebraic complexity.\r 9. Randomized algorithms, complexity classes of randomized algorithms (classes BPP, ZP, RP).\r 10. One-way functions, pseudorandom sequences, discrete logarithm, cryptography.\r 11. Interactive proofs, probabilistically verifiable proofs, expanders, gap problem, PCP theorem, non-aproximability of 3SAT.\r Seminar syllabus:
1. Mutual simulations of computational models. 2. [2] NP-complete problems and their reductions. 3. Particular problems in coNP and NP intersection coNP. 4. [2] Complete problems for PSPACE and different classes of the hierarchy in PSPACE. 5. [2] Examples of circuits for different simple problems, bounded fan-in. 6. [3] Examples of different Monte-Carlo and Las Vegas algorithms. 7. Examples of pseudorandom sequences ans simple facts about their (non-)predictability. 8. Amplification of a success probability, examples of randomized algorithms. 9. Expanders and random walks, Markov chains and their mixing. Literature:
1. Arora, S., Barak, B. ''Computational Complexity: A Modern Approach''. Cambridge University Press, 2009. ISBN 0521424267. 2. Goldreich, O. ''Computational Complexity: A Conceptual Perspective''. Cambridge University Press, 2008. ISBN 052188473X. 3. Motwani, R., Raghavan, P. ''Randomized Algorithms''. Cambridge University Press, 1995. ISBN 0521474655. Requirements:
Informace o předmětu a výukové materiály naleznete na https://courses.fit.cvut.cz/MI-CPX/ The course is also part of the following Study plans:
Study Plan Study Branch/Specialization Role Recommended semester MI-WSI-WI.2016 Web and Software Engineering V 3 MI-SP-SP.2016 System Programming V 3 MI-WSI-ISM.2016 Web and Software Engineering V 3 MI-PSS.2016 Computer Systems and Networks V 3 MI-NPVS.2016 Design and Programming of Embedded Systems V 3 MI-ZI.2016 Knowledge Engineering V 3 MI-ZI.2018 Knowledge Engineering V 3 MI-WSI-ISM.2016 Web and Software Engineering V 3 MI-SP-TI.2016 System Programming PZ 3 MI-WSI-SI.2016 Web and Software Engineering V 3 MI-SPOL.2016 Unspecified Branch/Specialisation of Study VO 3
Page updated 19. 4. 2024, semester: L/2020-1, L/2021-2, Z/2023-4, Z/2024-5, Z/2019-20, Z/2022-3, L/2019-20, L/2022-3, Z/2020-1, Z/2021-2, L/2023-4, Send comments to the content presented here to Administrator of study plans Design and implementation: J. Novák, I. Halaška