Course details

# Theoretical Computer Science

TIN Acad. year 2005/2006 Winter semester 5 credits

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Language of instruction

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Time span

Assessment points

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Lecturer

Instructor

Subject specific learning outcomes and competences

Learning objectives

Prerequisite kwnowledge and skills

Study literature

- 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

Fundamental literature

- 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
- Martin, J.C.: Introduction to Languages and the Theory of Computation, McGraw-Hill, Inc., 3rd ed., 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

Syllabus of lectures

- 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.

Syllabus - others, projects and individual work of students

- 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.

Progress assessment