Course detail

Theoretical Computer Science

FIT-TINAcad. year: 2025/2026

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, and the introduction to logics and complexity theory.

Language of instruction

Czech

Number of ECTS credits

7

Mode of study

Not applicable.

Guarantor

doc. RNDr. Milan Češka, Ph.D.

Department

Department of Intelligent Systems (UITS)

Entry knowledge

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

Rules for evaluation and completion of the course

The evaluation of the course consists of the test in the 4th week (max. 15 points) and the test in the 8th week (max. 15 points), the 2 assignments (max 7 points and 8 points, respectively), and the final exam (max 60 points).

The written test in the 4th week focuses on the regular languages. The written test in the 8th week focuses on context-free languages, and decidability including constructions of Turing machines and basic concepts of computational complexity.

The requirements to obtain the accreditation that is required for the final exam: The minimal total score of 18 points achieved from the assignments and from the tests in the 4th and 8th week (i.e. out of 40 points).

The final exam has 4 parts. Students have to achieve at least 4 points from each part and at least 25 points in total, otherwise the exam is evaluated by 0 points.

 

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.

 

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 acquire basic capabilities for theoretical research activities.

Study aids

Prerequisites and corequisites

Not applicable.

Basic literature

Aho, A.V., Ullmann, J.D.: The Theory of Parsing,Translation and Compiling, Prentice-Hall, 1972. ISBN 0-139-14564-8
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
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
Martin, J.C.: Introduction to Languages and the Theory of Computation, McGraw-Hill, Inc., 3rd ed., 2002. ISBN 0-072-32200-4

Recommended reading

Aho, A.V., Ullmann, J.D.: The Theory of Parsing,Translation and Compiling, Prentice-Hall, 1972. ISBN 0-139-14564-8
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
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
Češka, M., Vojnar, T.: Studijní  text k předmětu Teoretická informatika (http://www.fit.vutbr.cz/study/courses/TIN/public/Texty/TIN-studijni-text.pdf), 165 str. (in Czech)
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
Martin, J.C.: Introduction to Languages and the Theory of Computation, McGraw-Hill, Inc., 3rd ed., 2002. ISBN 0-072-32200-4
Meduna, A.: Formal Languages and Computation. New York, Taylor & Francis, 2014.

Classification of course in study plans

  • Programme MITAI Master's

    specialization NSEC , 1 year of study, winter semester, compulsory
    specialization NISY up to 2020/21 , 1 year of study, winter semester, compulsory
    specialization NNET , 1 year of study, winter semester, compulsory
    specialization NMAL , 1 year of study, winter semester, compulsory
    specialization NCPS , 1 year of study, winter semester, compulsory
    specialization NHPC , 1 year of study, winter semester, compulsory
    specialization NVER , 1 year of study, winter semester, compulsory
    specialization NIDE , 1 year of study, winter semester, compulsory
    specialization NISY , 1 year of study, winter semester, compulsory
    specialization NEMB , 1 year of study, winter semester, compulsory
    specialization NSPE , 1 year of study, winter semester, compulsory
    specialization NEMB , 1 year of study, winter semester, compulsory
    specialization NBIO , 1 year of study, winter semester, compulsory
    specialization NSEN , 1 year of study, winter semester, compulsory
    specialization NVIZ , 1 year of study, winter semester, compulsory
    specialization NGRI , 1 year of study, winter semester, compulsory
    specialization NADE , 1 year of study, winter semester, compulsory
    specialization NISD , 1 year of study, winter semester, compulsory
    specialization NMAT , 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

39 hod., optionally

Teacher / Lecturer

doc. Mgr. Lukáš Holík, Ph.D.
doc. RNDr. Milan Češka, Ph.D.

Syllabus

  1. An introduction to the theory of formal languages, regular languages and grammars, finite  automata, regular expressions.
  2. Minimization of finite-state automata, pumping theorem, Nerod's theorem, decidable problems of regular languages.
  3. Context-free languages and grammars; push-down automata. Advanced properties of context-free languages, pumping theorem for context-free languages, decidable problems of context-free languages.
  4. Turing machines (TMs), the language accepted by a TM, recursively enumerable and recursive languages and problems.TMs and type-0 languages, properties of recursively enumerable and recursive languages, linearly bounded automata and type-1 languages. 
  5. An introduction to the computational complexity, Turing complexity, asymptotic complexity, complexity classes.
  6. Complexity analysis outside TM, amortized complexity, 
  7. Properties of complexity classes (P vs NP), polynomial reduction, problems beyond NP
  8. Regex Matching: from regular expressions, over automata and algorithms to complexity and security.
  9. The Church-Turing thesis, undecidability, the halting problem, reductions, Post's correspondence problem, undecidable problems of the formal language theory, diagonalization. 
  10. Axiomatization systems for predicate and propositional logic.
  11. Gödel's incompleteness theorems.
  12. Consultation.

Seminar

12 hod., optionally

Teacher / Lecturer

doc. Mgr. Adam Rogalewicz, Ph.D.
Ing. Ondřej Lengál, Ph.D.
doc. RNDr. Milan Češka, Ph.D.

Syllabus

  1. Review of discrete mathematics and formal languages.
  2. Regular languages.
  3. Context-free language, Turing machines and decidability
  4. Advanced complexity and polynomial reduction.
  5. Undecidability: use of reduction and diagonalization.
  6. Incompleteness of logical systems.

Fundamentals seminar

14 hod., optionally

Teacher / Lecturer

Ing. Ondřej Lengál, Ph.D.
doc. Mgr. Adam Rogalewicz, Ph.D.
doc. RNDr. Milan Češka, Ph.D.

Syllabus

  1. Regular languages.
  2. An introduction to context-free languages.
  3. Context-free language, Turing machines and decidability.
  4. Asymptotic and amortized complexity analysis.
  5. Advanced complexity and polynomial reduction.
  6. Undecidability: use of reduction.
  7. Logical systems.

Project

13 hod., compulsory

Teacher / Lecturer

doc. Mgr. Adam Rogalewicz, Ph.D.
Ing. Ondřej Lengál, Ph.D.

Syllabus

  1. Assignment  in the area of regular and contex-free languages.
  2. Assignment  in the area of context-free languages and Turing machines.
  3. Assignment  in the area of undecidability and complexity.