460-2005/05 – Introduction to Theoretical Computer Science (UTI)
| Gurantor department | Department of Computer Science | Credits | 6 |
| Subject guarantor | doc. Ing. Zdeněk Sawa, Ph.D. | Subject version guarantor | doc. Ing. Zdeněk Sawa, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 2 | Semester | summer |
| | Study language | Czech |
| Year of introduction | 2018/2019 | Year of cancellation | 2022/2023 |
| Intended for the faculties | FEI | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
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.
Teaching methods
Lectures
Tutorials
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.
Compulsory literature:
- Sawa, Z.: Introduction to Theoretical Computer Science (available on http://www.cs.vsb.cz/sawa/uti/slides/uti-en.pdf)
Recommended literature:
- 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.
Additional study materials
Way of continuous check of knowledge in the course of semester
Requirements during a semester:
- A written test during a semester (for 22 points)
Requirements for a credit:
- To get a credit, a student must obtain from the written test at least 7 points.
The exam:
- The exam is of a written form.
The exam consists of three parts devoted to the following areas:
- introduction to logic
- theory of formal languages and automata
- computability and complexity
It is possible to get 78 points for the exam.
To pass out the exam it is necessary to get at least 10 points from each of its parts.
E-learning
Other requirements
Additional requirements are placed on the student.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Lectures:
- Introduction. Logic. Proofs. Logical connectives.
- Other logical connectives. Syntax and semantics in logic.
- Table method. Equivalent transformations. Predicate logic.
- Quantifiers. Naive set theory.
- Formal languages - basic notions (an alphabet, a word, a language). Operations
on languages. Finite automata.
- Construction of finite automata. Nondeterinistic finite automata.
- Transformation of nondeterministic finite automata to deterministic.
Regular expressions.
- Context-free grammar and languages.
- Algorithmic problems. Models of computation (Turing machines and RAM machines).
- Asymptotic notation. Complexity of algorithms.
- Complexity of problems. Complexity classes. Reductions between problems. NP-complete
problems.
- Algorithmically undecidable problems.
Tutorials:
- Recalling of basics of the set theory, relations, functions and the graph theory.
- Propositional and predicate logic.
- Analysis of sentences of a natural language in the language of propositional and predicate logic.
- Deduction of consequences. Set theoretical / semantic proofs.
- Resolution method.
- Operations with languages.
- Construction of finite automata.
- Transformation of nondeterministic automata to deterministic.
- Regular expressions.
- Context-free grammars.
- Turing machines and RAM machines.
- Asymptotic notation. Complexity of algorithms.
- Complexity of problems. Complexity classes.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction