Course detail

# Theoretical Computer Science

FIT-TINAcad. year: 2017/2018

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
- 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, 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

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

Language of instruction

Czech

Work placements

Not applicable.

Course curriculum

- 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.
- 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.

**Syllabus of lectures:**

**Syllabus - others, projects and individual work of students:**

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, a final exam. **The minimal number of points which can be obtained from the final exam is 25. Otherwise, no points will be assign to a student.**

Classification of course in study plans

- Programme IT-MGR-2 Master's
branch MBI , 1. year of study, winter semester, 5 credits, compulsory

branch MPV , 1. year of study, winter semester, 5 credits, compulsory

branch MGM , 1. year of study, winter semester, 5 credits, compulsory

branch MSK , 1. year of study, winter semester, 5 credits, compulsory

branch MIS , 1. year of study, winter semester, 5 credits, compulsory

branch MBS , 1. year of study, winter semester, 5 credits, compulsory

branch MIN , 1. year of study, winter semester, 5 credits, compulsory

branch MMI , 1. year of study, winter semester, 5 credits, compulsory

branch MMM , 1. year of study, winter semester, 5 credits, compulsory