Theory of Algorithms

B232 - Summer 23/24
You don't have access to the course
B202 - Summer 20/21 B212 - Summer 21/22 B222 - Summer 22/23 B232 - Summer 23/24

Theory of Algorithms - BE4M01TAL

Student survey results
Credits 6
Semesters Summer
Completion Assessment + Examination
Language of teaching English
Extent of teaching 3P+2S
Annotation
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.
Study targets
No data.
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 outlines
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] Talbot, J., Welsh, D.: Complexity and Cryptography, Cambridge University Press, 2006
Requirements
No data.