Course detail

Theoretical Computer Science

FIT-TINAcad. year: 2010/2011

Not applicable.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

prof. RNDr. Milan Češka, CSc.

Department

Department of Intelligent Systems (UITS)

Learning outcomes of the course unit

Not applicable.

Prerequisites

Not applicable.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

Not applicable.

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

Not applicable.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme IT-MGR-2 Master's

    branch MBI , 1. year of study, winter semester, compulsory
    branch MPV , 1. year of study, winter semester, compulsory
    branch MGM , 1. year of study, winter semester, compulsory
    branch MSK , 1. year of study, winter semester, compulsory
    branch MPS , 1. year of study, winter semester, compulsory
    branch MIS , 1. year of study, winter semester, compulsory
    branch MBS , 1. year of study, winter semester, compulsory
    branch MIN , 1. year of study, winter semester, compulsory
    branch MMI , 1. year of study, winter semester, compulsory
    branch MMM , 1. year of study, winter semester, compulsory

Type of course unit

 

Lecture

39 hours, optionally

Teacher / Lecturer

prof. RNDr. Milan Češka, CSc.

Syllabus

  1. An overview of the applications of the formal language theory, the modelling and decision power of formalisms, operations over languages.
  2. Regular languages and their properties, Kleene's theorem, Nerod's theorem, Pumping lemma.
  3. Minimalization of finite-state automata, the relation of indistinguishability of automata states, construction of a reduced finite-state automaton.
  4. Closure properties of regular languages, regular languages as a Boolean algebra, decidable problems of regular languages.
  5. Context-free languages and their properties, normal forms of context-free grammars, unambiguous and deterministic context-free languages, Pumping lemma for context-free languages.
  6. Closure properties of context-free languages, closedness wrt. substitution and its consequences, decidable problems of context-free languages.
  7. Turing machines (TMs), the language accepted by a TM, recursively enumerable and recursive languages and problems, TMs and functions, methods of  constructing TMs.
  8. 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.
  9. TMs and type-0 languages, diagonalisation, properties of recursively enumerable and recursive languages, linearly bounded automata and type-1 languages.
  10. Computable functions, initial functions, primitive recursive functions, mu-recursive functions, the relation of TMs and computable functions.
  11. The Church-Turing thesis, universal TMs, undecidability, the halting problem, reductions, the Post's correspondence problem.
  12. Undecidable problems of the formal language theory.
  13. An introduction to the computational complexity, Turing complexity, the P and NP classes and beyond.

Project

13 hours, optionally

Teacher / Lecturer

prof. RNDr. Milan Češka, CSc.