Theoretical Computer Science

The course is a substitute for:

Theoretical Computer Science (X36TIN)

Lecturer:

Tutor:

Supervisor:

Department of Computer Science and Engineering

Synopsis:

The course reinforces abstraction and proof techniques in discrete structures presenting basic notions and problems of graph theory. Standard graph algorithms (as e.g. breadth-first and depth-first graph traversal, shortest paths algorithms of Dijkstra, Bellman-Ford, Floyd-Warshall, and Johnson, shortest spanning tree algorithms of Kruskal-Boruvka and Prim-Jarnik, max-flow algorithm of Ford-Fulkerson, etc.) are introduced and their complexity discussed. The course includes greedy algorithms and dynamic programming technique, complexity theory (P and NP complexity classes, NP-completeness), search problems in artificial intelligence, mathematical models of programs and computations (finite automata, Turing machines).

Requirements:

Students must undergo the initial test which checks their understanding of

basic data structures and the ways the structures are manipulated.

Those who fail to pass the test will not be permitted to enroll the subject.

The expected knowledge is:

Data types Queue, Stack, List, Binary Tree.

Understanding asymptotic complexity of an algorithm.

Distinguishing between slow and fast sorting algorithms.

Recursive processing of all elements in a binary tree.

Syllabus of lectures:

1. Theoretical models, undirected graphs, basic properties

2. Directed graphs, strong connectivity, topological sort

3. Graph representation, breadth-first and depth-first traversals

4. Euler's graphs, dominating and independent sets, distance

5. Trees and spanning trees, circuits, minimum spanning trees, binary trees

6. Algorithms of Boruvka and Jarník, Huffman's coding

7. Shortest paths algorithms, dynamic programming

8. Flow networks, maximum flow in network

9. General problem solving, state space, heuristic search

10. Regular languages and finite automata

11. Turing machines - structure and behavior

12. Generalized Turing machines, undecidable problems

13. Complexity classes P and NP, NP-completeness

14. Reserved

Syllabus of tutorials:

1. Using basic tools of mathematics (proof, induction, recurrence)

2. Operational complexity of algorithms, calculations with recurrences

3. Undirected graphs - basic properties

4. Graph traversals, decomposition into components, homework

5. Directed graphs - basic properties, depth-first search

6. Decomposition into strong components, homework consultation

7. Dominance, independence, trees

8. Spanning trees, minimum spanning trees

9. Shortest paths

10. Application of dynamic programming

11. Maximal flow in network, heuristic search algorithms

12. Regular languages and finite automata

13. Non-determinism, homework consultation

14. Assessment

Study Objective:

Study materials:

1. Kolář, J.: Theoretical Computer Science. Prague: CTU Publishing House. 1998

2. Cormen, T.H. et al. : Introduction to Algorithms. Cambridge, Mass.: MIT Press. 1990

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Computer Technology- structured studies (compulsory course)