Course detail

# Theoretical Computer Science (in English)

FIT-TINeAcad. year: 2019/2020

An overview of the applications of the formal language theory in modern computer science and engineering (compilers, system modelling and analysis, linguistics, etc.), the modelling and decision power of formalisms, regular languages and their properties, minimalization of finite-state automata, context-free languages and their properties, Turing machines, properties of recursively enumerable and recursive languages, computable functions, undecidability, undecidable problems of the formal language theory.

Supervisor

Department

Learning outcomes of the course unit

The students are acquainted with basic as well as more advanced terms, approaches, and results of the theory of automata and formal languages and with basics of the theory of computability and complexity allowing them to better understand the nature of the various ways of describing and implementing computer-aided systems. The students are capable of applying the acquainted knowledge when solving complex theoretical as well as practical problems in the areas of system modelling, programming, formal specification and verification, and artificial intelligence.

The students acquire basic capabilities for theoretical research activities.

Prerequisites

Basic knowledge of discrete mathematics concepts including graph theory and formal languages concepts, and basic concepts of algorithmic complexity.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Češka, M. a kol.: Vyčíslitelnost a složitost, Nakl. VUT Brno, 1993. ISBN 80-214-0441-8

Češka, M., Rábová, Z.: Gramatiky a jazyky, Nakl. VUT Brno, 1992. ISBN 80-214-0449-3

Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation, Addison Wesley, 2nd ed., 2000. ISBN 0-201-44124-1

Kozen, D.C.: Automata and Computability, Springer-Verlag, New Yourk, Inc, 1997. ISBN 0-387-94907-0

Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation, Addison Wesley, 2. vydání, 2000. ISBN 0-201-44124-1

Martin, J.C.: Introduction to Languages and the Theory of Computation, McGraw-Hill, Inc., 3. vydání, 2002. ISBN 0-072-32200-4

Brookshear, J.G. : Theory of Computation: Formal Languages, Automata, and Complexity, The Benjamin/Cummings Publishing Company, Inc, Redwood City, California, 1989. ISBN 0-805-30143-7

Aho, A.V., Ullmann, J.D.: The Theory of Parsing,Translation and Compiling, Prentice-Hall, 1972. ISBN 0-139-14564-8

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

A mid-term exam evaluation (max. 20 points) and an evaluation of homeworks (max 20 points).

Exam prerequisites:

The minimal total score of 15 points gained out of the first three assignements and the mid-term exam (i.e. out of 35 points).

Language of instruction

English

Work placements

Not applicable.

Aims

To acquaint students with more advanced parts of the formal language theory, with basics of the theory of computability, and with basic terms of the complexity theory.

Specification of controlled education, way of implementation and compensation for absences

A written mid-term exam, a regular evaluation of homeworks.

#### Type of course unit

Lecture

39 hours, optionally

Teacher / Lecturer

Syllabus

- An overview of the applications of the formal language theory, the modelling and decision power of formalisms, operations over languages.

- Regular languages and their properties, Kleene's theorem, Nerod's theorem, Pumping lemma.

- Minimalization of finite-state automata, the relation of indistinguishability of automata states, construction of a reduced finite-state automaton.

- Closure properties of regular languages, regular languages as a Boolean algebra, decidable problems of regular languages.

- Context-free languages and their properties, normal forms of context-free grammars, unambiguous and deterministic context-free languages, Pumping lemma for context-free languages.

- Closure properties of context-free languages, closedness wrt. substitution and its consequences, decidable problems of context-free languages.

- Turing machines (TMs), the language accepted by a TM, recursively enumerable and recursive languages and problems, TMs and functions, methods of constructing TMs.

- Modifications of TMs, TMs with a tape infinite on both sides, with more tapes, nondeterministic TMs, automata with two push-down stacks, automata with counters.

- TMs and type-0 languages, diagonalisation, properties of recursively enumerable and recursive languages, linearly bounded automata and type-1 languages.

- Computable functions, initial functions, primitive recursive functions, mu-recursive functions, the relation of TMs and computable functions.

- The Church-Turing thesis, universal TMs, undecidability, the halting problem, reductions, the Post's correspondence problem.

- Undecidable problems of the formal language theory.

- An introduction to the computational complexity, Turing complexity, the P and NP classes and beyond.

Projects

13 hours, compulsory

Teacher / Lecturer

Syllabus

- A homework on regular languages and finite-state automata.

- A homework on context-free languages.

- A homework on Turing machines.

- A homework on computable functions.

eLearning

**eLearning:** currently opened course