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Faculty of Electrical Engineering and Computer Science

ECTS Course Overview



Introduction to Theoretical Computer Science

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code460-2005/04
Number of ECTS Credits Allocated5 ECTS credits
Type of Course Unit *Optional
Level of Course Unit *First Cycle
Year of Study *
Semester when the Course Unit is deliveredSummer Semester
Mode of DeliveryFace-to-face
Language of InstructionEnglish
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
SAW75doc. Ing. Zdeněk Sawa, Ph.D.
Summary
The subject is an indroductory course of some basic areas of theoretical
computer science. Students get acquainted with essentials of logic, formal languages, automata, and computational complexity, together with some of their applications for solving problems in programming.
In particular, students will learn essentials of propositional and predicate logic. They will be able to formalize propositions in terms of these logics and to use some of methods of logical deduction.
They will learn about the use of finite automata, regular expressions and context-free grammars in the construction of compilers (in lexical and syntax analysis) and also for searching in text data. Students will learn some basics of the theory of computation and of the complexity theory. They will be able to analyze the computational complexity of algorithms and to use the asymptotic notation. Also the computational complexity of algorithmic problems and complexity classes will be mentioned briefly. Students will learn that some problems are computationally undecidable and how this
can be proved.
Learning Outcomes of the Course Unit
A student understands the basic terms of theoretical computer science, and can use them in programming. Moreover, the subject gives necessary background for further study of computer science at higher levels.

Course Contents
Lectures:

1. Introduction. What are the main topics of theoretical computer science (algorithms, algorithmic problems, formal languages, ...).
2. Formal languages - basic notions (alphabet, word, language). Operations on languages. Regular expressions.
3. Deterministic finite automata (DFA). Construction of DFA. Some language operations on DFA.
4. Nondeterministic finite automata (NFA). Transformation of NFA to DFA. Language operations on NFA. Relation between regular expressions and finite automata.
5. Context-free grammars and languages.
6. Pushdown automata and their relation to context-free grammars. Chomsky hierarchy.
7. Algorithmic problems. Models of computation (Turing machines and RAM machines). Church-Turing thesis.
8. Correctness of algorithms. Methods for proving correctness of algorithms.
9. Computational complexity of algorithms. Asymptotic notation. Analysis of computational complexity of algorithms (iterative and recursive).
10. General techniques used in design of algorithms - brute-force solution, divide-and-conquer, backtracking, greedy algorithms, dynamic programming.
11. Complexity of problems. Complexity classes (in particular classes P and NP). Reductions between problems. NP-complete problems.
12. Examples of NP-complete problems and reductions between problems.
13. Undecidable problems (e.g., halting problem).

Tutorials:
(Remark: The topics of tutorials correspond to the topics of lectures.)

1. Recalling basics of logic, set theory, relations, functions, and graph theory.
2. Operations on languages. Regular expressions.
3. Construction of deterministic finite automata (DFA). Operation on these automata.
4. Construction of nondeterministic finite automata (NFA). Transformation of NFA to DFA. Transformations between regular expressions and finite automata.
5. Construction of context-free grammars. Operations on these grammars.
6. Pushdown automata.
7. Algorithmic problems. Turing machines and RAM machines.
8. Proving correctness of algorithms.
9. Asymptotic notation. Analysis of computational complexity of algorithms.
10. Techniques of design of algorithms.
11. Complexity of problems. Complexity classes. Reductions between problems.
12. Proving NP-completeness of problems.
13. Proving undecidability of problems.
Recommended or Required Reading
Required Reading:
- Sawa, Z.: Introduction to Theoretical Computer Science (available on http://www.cs.vsb.cz/sawa/uti/slides/uti-en.pdf)
- doc. Ing. Zdeněk Sawa, Ph.D.: Úvod do teoretické informatiky - slidy (k dispozici na adrese http://www.cs.vsb.cz/sawa/uti/slides/uti-cz.pdf,
anglická verze na adrese http://www.cs.vsb.cz/sawa/uti/slides/uti-en.pdf)
- doc. Ing. Zdeněk Sawa, Ph.D.: Úvod do teoretické informatiky - logika a algoritmy, (k dispozici na adrese http://www.cs.vsb.cz/sawa/uti/materialy/uti-2014.02.09.pdf)
- prof. RNDr. Petr Jančar, CSc.: Úvod do teoretické informatiky - učební
text, 2007, (k dispozici na adrese http://www.cs.vsb.cz/sawa/uti/materialy/uti.pdf).
- doc. RNDr. Marie Duží, CSc.: Matematická logika, (k dispozici na adrese
http://www.cs.vsb.cz/sawa/uti/materialy/Matlogika.pdf).
Recommended Reading:
- Sipser, M.: Introduction to the Theory of Computation PWS Publishing Company, 1997.
- Kozen, D.: Automata and Computability. Undergraduate Text in Computer Science, Springer Verlag, 1997.
- Huth, M., Ryan, M.: Logic in Computer Science: Modelling and Reasoning about Systems, Cambridge University Press, 2004.- Papadimitriou, C.: Computational Complexity, Addison Wesley, 1993.
- Hopcroft, J.E., Motwani, R., Ullman, J, D.: Introduction to Automata Theory, Languages, and Computation (3rd Edition), Addison Wesley, 2006.
- Gruska, J.: Foundation of Computing. International Thomson Computer Press, 1997.
- Suppes, P.: Introduction to Logic, Dover Publications, 1999.
- Tarski, A.: Introduction to Logic and to the Methodology of Deductive Sciences, Dover Publications, 1995.
- Devlin, K.: Introduction to Mathematical Thinking, Keith Devlin, 2012.
- Sipser, M.: Introduction to the Theory of Computation, PWS Publishing Company, 1997.
- Kozen, D.: Automata and Computability. Undergraduate Text in Computer Science, Springer Verlag, 1997.
- Papadimitriou, C.: Computational Complexity, Addison Wesley, 1993.
- Hopcroft, J.E., Motwani, R., Ullman, J, D.: Introduction to Automata Theory, Languages, and Computation (3rd Edition), Addison Wesley, 2006.
- Gruska, J.: Foundation of Computing. International Thomson Computer Press, 1997.
- Huth, M., Ryan, M.: Logic in Computer Science: Modelling and Reasoning about Systems, Cambridge University Press, 2004.
- Švejdar, V.: Logika - neúplnost, složitost a nutnost, Academia, 2002.
- Suppes, P.: Introduction to Logic, Dover Publications, 1999.
- Tarski, A.: Introduction to Logic and to the Methodology of Deductive Sciences, Dover Publications, 1995.
- Devlin, K.: Introduction to Mathematical Thinking, Keith Devlin, 2012.
Planned learning activities and teaching methods
Lectures, Tutorials
Assesment methods and criteria
Tasks are not Defined