Subject description - AD4M01TAL

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AD4M01TAL Theory of Algorithms
Roles:ZZ, P, V Extent of teaching:21+3
Department:13101 Language of teaching:CS
Guarantors:  Completion:Z,ZK
Lecturers:  Credits:6
Tutors:  Semester:L


The course brings theoretical background of the theory of algorithms with the focus at first on the time and space complexity of algorithms and problems, secondly on the correctness of algorithms. Further it is dealt with the theory of complexity; the classes P, NP, NP-complete, PSPACE and NPSPACE are treated and properties of them investigated. Probabilistic algorithms are studied and the classes RP and ZZP introduced.

Course outlines:

1. Analyzing algorithms and problems, classifying functions by their growth rates, time and space complexity.
2. Correctness of algorithms, variants and invariants.
3. Decision problems and optimization problems.
4. Turing machine and its variants.
5. Relation between Turing machine and RAM machine.
6. Classes P and NP.
7. Reduction and polynomial reduction of problems.
8. NP-complete problems, Cook's Theorem.
9. Classes PSPACE and NPSPACE..
10. Randomized algorithms with polynomial time complexity.
11. Classes RP and ZZP.
12. Undecidable problems.
13. Reserve.

Exercises outline:

1. Determining time and space complexity of well known algorithms.
2. Verifying correctness of algorithms using variants and invariants.
3. Turing machines.
4. Polynomial reductions of problems.
5. Examples of randomized algorithms.
6. Examples of undecidable problems.


[1] Kozen, D. C.: The design and Analysis of Algorithms, Springer-Vrelag, 1991
[2] Harel, D: Algorithmics: The Spirit of Computing, Addison-Wesleyt Inc., Reading MA 2002
[3] Hopcroft, J., Motwani, R., Ullman, J.: Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, 2001


Logic and Graphs, Discrete Mathematics

Subject is included into these academic programs:

Program Branch Role Recommended semester
MKEEM1 Technological Systems V 2
MKEEM5 Economy and Management of Electrical Engineering V 2
MKEEM4 Economy and Management of Power Engineering V 2
MKEEM3 Electrical Power Engineering V 2
MKEEM2 Electrical Machines, Apparatus and Drives V 2
MKKME1 Wireless Communication V 2
MKKME5 Systems of Communication V 2
MKKME4 Networks of Electronic Communication V 2
MKKME3 Electronics V 2
MKKME2 Multimedia Technology V 2
MKOI1 Artificial Intelligence P 2
MKOI5 Software Engineering P 2
MKOI4 Computer Graphics and Interaction P 2
MKOI3 Computer Vision and Image Processing P 2
MKOI2 Computer Engineering P 2
MVT04N-D Computer Science and Engineering ZZ 2
MVT01N-D Computer Science and Engineering ZZ 2
MKKYR4 Aerospace Systems V 2
MKKYR1 Robotics V 2
MKKYR3 Systems and Control V 2
MKKYR2 Sensors and Instrumentation V 2

Page updated 14.6.2021 19:52:31, semester: L/2021-2, L/2020-1, Z,L/2022-3, Z/2021-2, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)