Course details

# Theoretical Computer Science Seminar

STI Acad. year 2018/2019 Winter semester 2 credits

The course has a form of practical demonstration exercises with an active participation of the students in solving various concrete problems from the areas of the theory of formal languages and automata as well as the theory of computability and complexity. The examples being solved fall into the areas of advanced theory and applications of regular languages, context-free and context languages, Turing machines, decidability, reductions of decidability problems, computable functions, and basics of complexity. The application areas include modeling of systems, formal analysis and verification, compilers, artificial intelligence, linguistics, etc.

Guarantor

Language of instruction

Completion

Time span

Department

Lecturer

Holík Lukáš, Mgr., Ph.D. (DITS FIT BUT)

Rogalewicz Adam, doc. Mgr., Ph.D. (DITS FIT BUT)

Vojnar Tomáš, prof. Ing., Ph.D. (DITS FIT BUT)

Subject specific learning outcomes and competences

A deeper understanding and an ability to apply knowledge from the theory of formal languages and the theory of computability and complexity. A student is able to apply the acquired knowledge when solving theoretical as well as practical problems in modelling of systems, programming, formal specification, design automation, verification, and/or artificial intelligence.

Generic learning outcomes and competences

Broader and deeper abilities to formalize and solve problems of computer science as well as engineering, design algorithms as well as construct proofs. A student also acquires better abilities for research in various areas of computer science.

Learning objectives

To broaden student abilities to apply advanced knowledge from the theory of formal languages and automata as well as the theory of computability and complexity, and abilities to solve concrete theoretical as well as practical problems from the given area. The course covers, broadens, and practices all areas discussed in the course of Theoretical Computer Science, i.e., regular languages and finite automata, context-free languages and push-down automata, Turing machines, computability, recursive functions as well as complexity.

Prerequisite kwnowledge and skills

Basic knowledge of the theory of algebra, graphs, as well as regular and context-free languages.

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
- Gruska, J.: Foundations of Computing, International Thomson Computer Press, 1997. ISBN 1-85032-243-0

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 seminars

- Sets and relations. Strings, languages, and operations over them. Grammars, the Chomsky hierarchy of grammars and languages.
- Regular languages and finite-state automata (FSA), determinization and minimization of FSA, conversion of regular expressions to FSA.
- Kleene algebra. Pumping lemma, proofs of non-regularity of languages.
- Context-free languages and grammars. Transformations of context-free grammars.
- Operations on context-free languages and their closure properties. Pumping lemma for context-free languages.
- Push-down automata, (nondeterministic) top-down and bottom-up syntax analysis. Deterministic push-down languages.
- Turing machines.
- Recursive and recursively enumerable languages and their properties.
- Decidability, semi-decidability, and undecidability of problems, reductions of problems.
- Computable functions. Other Turing-complete computing mechanisms (automata with multiple push-down stacks, counter automata).
- Complexity classes. Properties of space and time complexity classes.
- NP problems. Polynomial reduction.
- Applications of results of theoretical computer science in compilers, automated verification, linguistics, etc. An overview of various areas extending the discussed subjects (automated learning of languages from patterns, tree languages with applications in verification or in XML manipulations, counter automata with constraints, hierarchies of undecidable problems, ...).

Controlled instruction

The participation of students is checked; a student can miss at most two lectures without a proper justification.

Exam prerequisites

A student can miss at most two lectures without a proper justification.

Course inclusion in study plans