Course detail

# Theoretical Computer Science

FIT-TINAcad. year: 2018/2019

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, introduction to complexity theory and Petri nets.

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

- 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
- Reisig, W.: Petri Nets, An Introduction, Springer Verlag, 1985. ISBN: 0-387-13723-8

- 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
- Češka, M.: Petriho sítě, Akad.nakl. CERM, Brno, 1994. ISBN: 8-085-86735-4

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

An evaluation of the exam in the 3rd
week (max. 20 points) and in the 9th week (max. 15 points), an
evaluation of the assignments (max 3-times 5 points) and an final exam
evaluation (max 60 points).

Exam prerequisites:

The minimal total score
of 15 points achieved from the first two assignments, and from the exams in the
3rd and 9th week (i.e. out of 35 points).

Language of instruction

Czech

Work placements

Not applicable.

Course curriculum

- An introduction to the theory of formal languages, regular languages and grammars, finite automata, regular expressions.
- Context-free languages and grammars, push-down automata.
- Regular languages as a Boolean algebra, Kleene's algebra, Kleene's theorem, minimization of finite-state automata.
- Pumping lemma, Nerod's theorem, decidable problems of regular languages. Transformations and normal forms of context-free grammars
- Advanced properties of context-free languages, Pumping lemma for context-free languages, decidable problems of context-free languages. Deterministic 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, diagonalization, properties of recursively enumerable and recursive languages, linearly bounded automata and type-1 languages.
- The Church-Turing thesis, universal TMs, undecidability, the halting problem, reductions, Post's correspondence problem. Undecidable problems of the formal language theory.
- Computable functions, initial functions, primitive recursive functions, mu-recursive functions, the relation of TMs and computable functions, asymptotic complexity.
- An introduction to the computational complexity, Turing complexity,
- P and NP classes, and beyond. Polynomial reduction, Completeness.
- Introduction to Petri nets, motivations, definition of P/T Petri nets, methods of Petri net analyses, Petri net classes.
- Assignment in the area of regular and context free languages.
- Assignment in the area of Turing machines and the theory of undecidability.
- Assignment in the area of computable functions, complexity, and Petri nets.

**Syllabus of lectures:**

[The first two lectures summarize and formalize the body of knowledge acquired in the IFJ course. Lectures 3-5 deepen the knowledge in the area of regular and context-free languages. Lectures 6-12 introduce the fundamental
principles and concepts in the area of computability and complexity of formal
languages and problems. The last lecture
introduces the fundamental principles in the area of mathematical description, modeling,
and analysis of parallel and distributed dynamical systems using Petri Nets.]**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 exam in the 3rd
week focusing on the fundamental knowledge in the area of regular and
context-free languages, a written exam in the 9th week focusing on advance
topics in the area of regular and context-free languages, and on Turing
machines, regular evaluation of the assignments, a final written exam. **Students
have to achieve at least 25 points, otherwise the exam is assessed by 0 points.**

** **

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

#### Type of course unit

Lecture

39 hours, optionally

Teacher / Lecturer

Syllabus

- An introduction to the theory of formal languages, regular languages and grammars, finite automata, regular expressions.
- Context-free languages and grammars, push-down automata.
- Regular languages as a Boolean algebra, Kleene's algebra, Kleene's theorem, minimization of finite-state automata.
- Pumping lemma, Nerod's theorem, decidable problems of regular languages. Transformations and normal forms of context-free grammars
- Advanced properties of context-free languages, Pumping lemma for context-free languages, decidable problems of context-free languages. Deterministic 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, diagonalization, properties of recursively enumerable and recursive languages, linearly bounded automata and type-1 languages.
- The Church-Turing thesis, universal TMs, undecidability, the halting problem, reductions, Post's correspondence problem. Undecidable problems of the formal language theory.
- Computable functions, initial functions, primitive recursive functions, mu-recursive functions, the relation of TMs and computable functions, asymptotic complexity.
- An introduction to the computational complexity, Turing complexity,
- P and NP classes, and beyond. Polynomial reduction, Completeness.
- Introduction to Petri nets, motivations, definition of P/T Petri nets, methods of Petri net analyses, Petri net classes.

[The first two lectures summarize and formalize the body of knowledge acquired in the IFJ course. Lectures 3-5 deepen the knowledge in the area of regular and context-free languages. Lectures 6-12 introduce the fundamental principles and concepts in the area of computability and complexity of formal languages and problems. The last lecture introduces the fundamental principles in the area of mathematical description, modeling, and analysis of parallel and distributed dynamical systems using Petri Nets.]

Project

13 hours, compulsory

Teacher / Lecturer

Syllabus

- Assignment in the area of regular and context free languages.
- Assignment in the area of Turing machines and the theory of undecidability.
- Assignment in the area of computable functions, complexity, and Petri nets.