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.
NI-CPX Complexity Theory Extent of teaching: 3P+1C Instructor: Knop D., Suchý O. 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 (in)tractability of difficult problems.
Lecture syllabus:
1. Computational problems and models of computation, Turing Machine, Undecideability. 2. Time hierarchy, non-deterministic Turing Machine. 3. Class NP, the existence of an NP-complete problem, Cook's theorem. 4. Strong and weak NP-hardness, pseudopolynomial algorithms, class coNP, Ladner's theorem. 5. Oracle Turing Machine, relativization, Baker-Gill-Solovay theorem. 6. Polynomial hierarchy, problems hard for classes of the hierarchy. 7. Space complexity, Class PSPACE, Savitch's Theorem, Logspace. 8. Boolean circuits, Circuit complexity, P/poly, circuits of bounded depth, paralelization of computation, P-completeness. 9. Probabilistic Turing Machine, Classes of randomized algorithms, error reduction, relations to P/poly and to Polynomial Hierarchy. 10. Optimalization problems, Approximation algorithms, Classes of approximability. 11. Probabilistically checkable proofs, PCP theorem, inaproximability of Vertex Cover and Independent Set. 12. Exponential Time Hypothesis (ETH), Strong ETH, their relations and implications. 13. Quantum Computation and relations to classical classes. Seminar syllabus:
1. Complexity of algorithms, simulation of models of computation in different model. 2. Non-determinism, class NP. 3. Problems outside NP, various NP-complete problems a reductions between them, problems in coNP. 4. Problems in PSPACE and various classes of the polynomial hierarchy, examples of circuits for various simple problems. 5. Amplification of success probability of randomized algorithms, examples of randomized algorithms. 6. Various approximation algorithms a proofs of inapproximability. Literature:
Goldreich, O. Computational Complexity: A Conceptual Perspective. Cambridge University Press, 2008. ISBN 052188473X.
S. Arora, B. Barak, ''Computational Complexity: A Modern Approach''. Cambridge University Press, 2009. ISBN 0521424267. Christos H. Papadimitriou, ?Computational Complexity?. Pearson, 1993. ISBN 978-0201530827
R. Motwani, P. Raghavan, ''Randomized Algorithms''. Cambridge University Press, 1995. ISBN 0521474655. M. Mitzenmacher, E. Upfal, '' Probability and Computing: Randomized Algorithms and Probabilistic Analysis''. Cambridge University Press, 2005, ISBN9780521835404.
D. P. Williamson, D. B. Shmoys: ?The Design of Approximation Algorithms?, Cambridge university press, 2011. ISBN 9780521195270 V. V. Vazirani: Approximation Algorithms, Springer, 2001. ISBN 3540653678 Requirements:
Knowledge of graph theory and graph algorithms in scope of BIE-AG1, as well as formal languages, Turing machines, P and NP classes, and nedeterminism in scope of BIE-AAG is assumed. Knowledge from BIE-AG2, such as Hamilton cycles, TSP, approximation algorithms, etc. is highly beneficial.
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 NI-PB.2020 Computer Security V 3 NI-ZI.2020 Knowledge Engineering V 3 NI-SPOL.2020 Unspecified Branch/Specialisation of Study V 3 NI-TI.2020 Computer Science V 3 NI-TI.2023 Computer Science V 3 NI-NPVS.2020 Design and Programming of Embedded Systems V 3 NI-PSS.2020 Computer Systems and Networks V 3 NI-MI.2020 Managerial Informatics V 3 NI-SI.2020 Software Engineering (in Czech) V 3 NI-SP.2020 System Programming V 3 NI-WI.2020 Web Engineering V 3 NI-SP.2023 System Programming V 3 NI-TI.2023 Computer Science PS Není
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