Automata and Grammars

In order to register for the course BIE-PJP.21, the student must have received credit for the course BIE-AAG.21 in a previous semester.

Garant předmětu:

Jan Holub

Lecturer:

Jan Holub

Tutor:

Štěpán Plachý

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, translation finite automata, construction and use of pushdown automata, hierarchy of formal languages, relationships between formal languages and automata. Knowledge acquired through the module is applicable in designs of algorithms for searching in text, data compression, simple parsing and translation, and design of digital circuits.

Requirements:

Knowledge of basic data structures and computer programming.

Syllabus of lectures:

1. Motivation to study formal languages. Basic notions (language, alphabet, grammar, automaton), Chomsky hierarchy.

2. Nondeterministic and deterministic finite automata (NFA, DFA), NFA with epsilon transitions.

3. Operations on automata (transformation to NFA without epsilon transitions, to DFA, minimization), intersection, union.

4. Programming implementations of DFA and NFA, circuit implementations.

5. Adding translation, Mealey, Moore, conversions.

6. Operations on regular grammars, conversions to FA.

7. Regular expressions, regular expression conversions, finite automata and regular grammars, Kleene theorem.

8. Principles of use of regular expressions in UNIX (grep, egrep, perl, PHP, ...).

9. Finite automaton as a lexical analyzer, lex/flex generators.

10. Properties of regular languages (pumping lemma, Nerode theorem).

11. Context-free languages, pushdown automaton.

12. Parsing of context-free languages (nondeterministic versus deterministic).

13. Context-sensitive and recursively enumerable languages, Turing machine. Classes P, NP, NPC, NPH

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.

Note:

Further information:

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

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Bachelor specialization, Computer Engineering, 2021 (compulsory course in the program)
• Bachelor specialization, Information Security, 2021 (compulsory course in the program)
• Bachelor specialization, Software Engineering, 2021 (compulsory course in the program)
• Bachelor specialization, Computer Science, 2021 (compulsory course in the program)
• Bachelor specialization, Computer Networks and Internet, 2021 (compulsory course in the program)
• Bachelor specialization Computer Systems and Virtualization, 2021 (compulsory course in the program)