# Subject description - AE4M01TAL

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 AE4M01TAL Theory of Algorithms Extent of teaching: 3+1 Guarantors: Roles: P,V Language ofteaching: EN Teachers: Completion: Z,ZK Responsible Department: 13101 Credits: 6 Semester: L

Anotation:

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.

Literature:

 [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

Requirements:

Logic and Graphs, Discrete Mathematics

Webpage:

http://math.feld.cvut.cz/demlova/teaching/e-tal_vyuka.html

Subject is included into these academic programs:

 Program Branch Role Recommended semester MEKME1 Wireless Communication V 2 MEKME5 Systems of Communication V 2 MEKME4 Networks of Electronic Communication V 2 MEKME3 Electronics V 2 MEKME2 Multimedia Technology V 2 MEOI1 Artificial Intelligence P 2 MEOI5NEW Software Engineering P 2 MEOI5 Software Engineering P 2 MEOI4 Computer Graphics and Interaction P 2 MEOI3 Computer Vision and Image Processing P 2 MEOI2 Computer Engineering P 2 MEEEM1 Technological Systems V 2 MEEEM5 Economy and Management of Electrical Engineering V 2 MEEEM4 Economy and Management of Power Engineering V 2 MEEEM3 Electrical Power Engineering V 2 MEEEM2 Electrical Machines, Apparatus and Drives V 2 MEKYR4 Aerospace Systems V 2 MEKYR1 Robotics V 2 MEKYR3 Systems and Control V 2 MEKYR2 Sensors and Instrumentation V 2

 Page updated 24.6.2019 17:52:59, semester: Z,L/2020-1, L/2018-9, Z,L/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)