Automata and Grammars

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Code	Completion	Credits (ECTS)	Range	Language
BI-AAG.21	Z,ZK	5	2P+2C	Czech

Course guarantor:

Jan Holub

Lecturer:

Jan Holub, Jan Janoušek

Tutor:

Suzan Catay, Filip Dilmaghani, František Dušek, Žaneta Genčiová, Albert Havliček, Jan Holub, Alina Ilchenko, Matěj Kříž, Tomáš Pecka, Šimon Rataj, Martin Svoboda, Ondřej Štorc

Supervisor:

Department of Theoretical Computer Science

Synopsis:

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.

Requirements:

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 course aims to familiarise students with finite automata, regular expressions, grammars and translation finite automata, with an emphasis on practical application. It will also introduce students to the class of context-free languages, the basic use of pushdown automata and the hierarchy of languages, to help them navigate the subject matter more easily. The knowledge gained in this course will be applicable in the design of algorithms for pattern matching, data compression, translation, simple syntactic analysis and the design of digital circuits.

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

Note:

Rozsah=prednasky+proseminare+cviceni2p+2c, Přednášející: doc. Ing. Jan Holub Ph.D.

Further information:

https://courses.fit.cvut.cz/BI-AAG/

Time-table for winter semester 2026/2027:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue	roomTK:BS Janoušek J. 11:00–12:30 (lecture parallel1) Dejvice roomT9:301 Dilmaghani F. 14:30–16:00 (parallel nr.1) Dejvice roomT9:301 Dilmaghani F. 16:15–17:45 (parallel nr.3) Dejvice roomTK:BS Holub J. 12:45–14:15 (lecture parallel2) Dejvice roomT9:346 Ilchenko A. 14:30–16:00 (parallel nr.2) Dejvice NBFIT schoolroom
Wed	roomTH:A-1242 Kříž M. 07:30–09:00 (parallel nr.22) Thákurova 7 (budova FSv) roomTH:A-942 Rataj Š. 12:45–14:15 (parallel nr.5) Thákurova 7 (budova FSv) roomT9:301 Havliček A. 16:15–17:45 (parallel nr.6) Dejvice roomT9:346 Štorc O. 07:30–09:00 (parallel nr.4) Dejvice NBFIT schoolroomroomT9:347 Rataj Š. 16:15–17:45 (parallel nr.7) Dejvice
Thu	roomT9:301 Štorc O. 07:30–09:00 (parallel nr.8) Dejvice roomT9:346 Catay S. 11:00–12:30 (parallel nr.10) Dejvice NBFIT schoolroomroomT9:301 Pecka T. 12:45–14:15 (parallel nr.11) Dejvice roomT9:301 Pecka T. 14:30–16:00 (parallel nr.13) Dejvice roomTH:A-942 Svoboda M. 16:15–17:45 (parallel nr.16) Thákurova 7 (budova FSv) roomTH:A-942 Svoboda M. 18:00–19:30 (parallel nr.17) Thákurova 7 (budova FSv) roomT9:347 Kříž M. 07:30–09:00 (parallel nr.9) Dejvice roomTH:A-942 Svoboda M. 12:45–14:15 (parallel nr.12) Thákurova 7 (budova FSv) roomTH:A-942 Svoboda M. 14:30–16:00 (parallel nr.14) Thákurova 7 (budova FSv)
Fri	roomTH:A-1442 Catay S. 07:30–09:00 (parallel nr.18) Thákurova 7 (budova FSv) roomT9:347 Genčiová Ž. 16:15–17:45 (parallel nr.19) Dejvice roomTH:A-1442 Genčiová Ž. 09:15–10:45 (parallel nr.20) Thákurova 7 (budova FSv) roomT9:347 Genčiová Ž. 14:30–16:00 (parallel nr.21) Dejvice

Time-table for summer semester 2026/2027:

Time-table is not available yet

The course is a part of the following study plans:

Bachelor Specialization Information Security, in Czech, 2021 (compulsory course in the program)
Bachelor Specialization Management Informatics, in Czech, 2021 (compulsory course in the program)
Bachelor Specialization Computer Graphics, in Czech, 2021 (compulsory course in the program)
Bachelor Specialization Computer Engineering, in Czech, 2021 (compulsory course in the program)
Bachelor program, unspecified specialization, in Czech, 2021 (compulsory course in the program)
Bachelor Specialization Web Engineering, in Czech, 2021 (compulsory course in the program)
Bachelor Specialization Artificial Intelligence, in Czech, 2021 (compulsory course in the program)
Bachelor Specialization Computer Science, in Czech, 2021 (compulsory course in the program)
Bachelor Specialization Software Engineering, in Czech, 2021 (compulsory course in the program)
Bachelor Specialization Computer Systems and Virtualization, in Czech, 2021 (compulsory course in the program)
Bachelor Specialization Computer Networks and Internet, in Czech, 2021 (compulsory course in the program)
Bachelor Specialization Information Security, in Czech, 2024 (compulsory course in the program)
Bachelor program, unspecified specialization, in Czech, 2024 (compulsory course in the program)
Bachelor Specialization Management Informatics, in Czech, 2024 (compulsory course in the program)
Bachelor Specialization Computer Graphics, in Czech, 2024 (compulsory course in the program)
Bachelor Specialization Software Engineering, in Czech, 2024 (compulsory course in the program)
Bachelor Specialization Web Engineering, in Czech, 2024 (compulsory course in the program)
Bachelor Specialization Computer Networks and Internet, in Czech, 2024 (compulsory course in the program)
Bachelor Specialization Computer Engineering, in Czech, 2024 (compulsory course in the program)
Bachelor Specialization Computer Systems and Virtualization, in Czech, 2024 (compulsory course in the program)
Bachelor Specialization Artificial Intelligence, in Czech, 2024 (compulsory course in the program)
Bachelor Specialization Computer Science, in Czech, 20214 (compulsory course in the program)
Bc. specialization Computer Graphics with omitting BI-SVZ (compulsory course in the program)