Automata and Grammars

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Code Completion Credits Range Language
BI-AAG.21 Z,ZK 5 2P+2C Czech
Garant předmětu:
Jan Holub
Jan Holub, Jan Janoušek
Dominika Draesslerová, Ondřej Guth, Tomáš Pecka, Štěpán Plachý, Martin Svoboda, Eliška Šestáková
Department of Theoretical Computer Science

Students are introduced to basic theoretical and implementation principles of the following topics: construction, use and mutual transformations of finite automata, regular expressions, and regular grammars, context-free grammars, construction and use of pushdown automata, and translation grammars and transducers. They know the hierarchy of formal languages and they understand the relationships between formal languages and automata. They are introduced to the Turing machine and complexity classes P and NP.


Knowledge of basic data structures and computer programming.

Syllabus of lectures:

1. Basic notions, Chomsky hierarchy.

2. Deterministic and nondeterministic finite automata.

3. Operations on automata.

4. Regular expressions.

5. Conversions between regular grammars, regular expressions, and finite automata.

6. Properties of regular languages.

7. Context-free grammars.

8. Pushdown automata. Parsing.

9. Translation grammars and transducers.

10. Context-sensitive, recursively enumerable and recursive languages. Turing machine.

11. Time complexity, classes P and NP.

12. Program and circuit implementation of finite automata.

13. Finite automaton as a lexical analyzer.

Syllabus of tutorials:

1. Implementation of FA.

2. Examples of formal languages. Intuitive considerations of grammars for given languages. Estimation of the classification of a given language in Chomsky hierarchy.

3. Intuitive creation of finite automata (DFA, NFA, with epsilon transitions) for a given langauage.

4. Transformations and compositions of FA.

5. FA with output function and its implementation.

6. Conversions of grammars to FA and vice versa.

7. Considerations, modifications and transformations of regular expressions.

8. Use of regular expressions for text processing tasks (e.g. sh, grep, sed, perl).

9. Creation and implementation of lexical analyzers.

10. Classification of languages.

11. Examples of context-free languages, creation of pushdown automata.

12. Examples of deterministic parsing of context-free languages (e.g. LL, yacc, bison).

13. Examples of context-sensitive and recursively enumerable languages, creation of grammars, creation of Turing machines.

Study Objective:

The module introduces students to finite automata, regular expressions, grammars, and translation finite automata, with an emphasis on their practical use. Furthermore, the module introduces students to the class of context-free languages, basic use of pushdown automata, as well as the classification of languages.

Study materials:

1. Sipser M. : Introduction to the Theory of Computation. Cengage Learning Custom Publishing, 2020. ISBN 978-0357670583.

2. Hopcroft J.E., Motwani R., Ullman J. D. : Introduction to Automata Theory, Languages, and Computation, 3rd Edition. Pearson, 2008. ISBN 978-8131720479.

3. Kozen D. C. : Automata and Computability. Springer, 1997. ISBN 978-0387949079.

4. Šestáková E.: Automaty a gramatiky: Sbírka řešených příkladů, ČVUT 2017, ISBN 978-80-01-06306-4

5. Šestáková E.: Automata and Grammars, A Collection of exercises and Solutions, ČVUT, 2018, ISBN 978-80-01-06462-7

Further information:
Time-table for winter semester 2024/2025:
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Time-table for summer semester 2024/2025:
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The course is a part of the following study plans:
Data valid to 2024-05-23
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