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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2022/2023

Automata in Text Pattern Matching

The course is not on the list Without time-table
Code Completion Credits Range Language
MI-AVY Z,ZK 4 2P+1C Czech
Lecturer:
Ondřej Guth (guarantor), Tomáš Pecka, Štěpán Plachý, Jan Trávníček, Jan Žďárek
Tutor:
Ondřej Guth (guarantor), Tomáš Pecka, Štěpán Plachý, Jan Trávníček, Jan Žďárek
Supervisor:
Department of Theoretical Computer Science
Synopsis:

Searching in a text (pattern matching) and generally in data is an area of problems and exciting solutions from theoretical and practical perspectives. We may interpret and search the data as one-dimensional (text) or multi-dimensional (tree, picture). We may search for something known (a pattern: a string or a set specified by regular expression) or unknown (for example, a regularity). Matching can be either exact or approximate. This course presents a taxonomy of searching problems. It focuses on algorithms based on some automaton (finite, pushdown, linear-bounded, or tree).

Requirements:

Students are supposed to know the formal language theory and algorithms on finite automata (BIE-AAG course). In particular, students should be familiar with Chomsky hierarchy of languages, subset construction and epsilon-transitions removal.

Syllabus of lectures:

1. Finite automata, basic operations with finite automata. Taxonomy of pattern matching problems for exact and approximate matching. Forward pattern matching, models of searching algorithms. Nondeterministic search automata.

2. Deterministic search finite automata and their state complexity.

3. Construction of prefix and suffix automata. Construction of factor automata. Computation of borders and periods of text. Searching exact and approximate repetitions in text.

4. Searching other string regularities and other indexing automata applications.

5. Regular expressions with backreferences.

6. Synchronizing finite automata.

7. Locally testable languages.

8. Classes of deterministic and nondeterministic pushdown automata. Determinisation of pushdown automata.

9. Tree automata.

10. Tree pattern matching & indexing, non-linear tree patterns.

11. Combinatorial pattern matching and indexing of multidimensional text.

12. Tree regular expressions.

Syllabus of tutorials:

1. Finite automata, basic operations with finite automata. Taxonomy of pattern matching problems for exact and approximate matching. Forward pattern matching, models of searching algorithms. Nondeterministic search automata.

2. Deterministic search finite automata and their state complexity.

3. Construction of prefix and suffix automata. Construction of factor automata. Computation of borders and periods of text. Searching exact and approximate repetitions in text.

4. Searching other string regularities and other indexing automata applications.

5. Regular expressions with backreferences.

6. Synchronizing finite automata.

7. Locally testable languages.

8. Classes of deterministic and nondeterministic pushdown automata. Determinisation of pushdown automata.

9. Tree automata.

10. Tree pattern matching & indexing, non-linear tree patterns.

11. Combinatorial pattern matching and indexing of multidimensional text.

12. Tree regular expressions.

Study Objective:

The students get familiar with algorithms for text, tree and image pattern matching. Those algorithms are based on finite, pushdown, linear-bounded, and tree automata. The students also get familiar with a taxonomy of pattern matching problems. They learn the principles of the construction of automata for solving these problems. The students can use this knowledge to develop applications for pattern matching (for example, DNA or data streams).

Study materials:

1. Melichar, B.; Holub, J.; Polcar, T. Text Searching Algorithms. Volume I: Forward String Matching. Dostupné z: https://psc.fit.cvut.cz/athens/TextSearchingAlgorithms/

2. Aho, A. V. Algorithms for Finding Patterns in Strings. In Handbook of Theoretical Computer Science, Algorithms and Complexity, 255-300. Elsevier, 1990. ISBN 9780444880710. DOI: 10.1016/B978-0-444-88071-0.50010-2.

3. Alur, R.; Madhusudan P. Visibly pushdown languages. In Proc. 36th Int. ACM Symposium on Theory of Computing (STOC), 2004.

4. Van Tang, N. A tighter bound for the determinization of visibly pushdown automata. In 11th International Workshop on Verification of Infinite-State Systems, INFINITY 2009, 2009.

5. Nowotka, D.; Srba J. Height-Deterministic Pushdown Automata. In 32nd International Symposium on Mathematical Foundations of Computer Science, MFCS'07, 2007.

6. Černý, J. Poznámka k homogénnym experimentom s konečnými automatmi. Matematicko-fyzikálny časopis Slovenskej Akadémie Vied, 14: 208-216. Dostupné z: https://dml.cz/handle/10338.dmlcz/126647

7. Pin, JE. On two combinatorial problems arising from automata theory. Combinatorial mathematics (Marseille-Luminy, 1981), 1983, Marseille-Luminy, pp.535-548. Dostupné z: https://hal.archives-ouvertes.fr/hal-00143937

8. Holub, J.; Štekr, S. Implementation of deterministic finite automata on parallel computers. Colloquium and Festschrift at the occasion of the 60th birthday of Derrick Kourie (Computer Science), Windy Brow, South Africa, 28 June 2008. Dostupné z: http://hdl.handle.net/2263/9145

9. Yechezkel, Z. Locally testable languages. Journal of Computer and System Sciences 6, 151-167 (1972). Dostupné z: https://doi.org/10.1016/S0022-0000(72)80020-5

10. James, R.; Dakotah, L. Extracting Forbidden Factors from Regular Stringsets. Proceedings of the 15th Meeting on the Mathematics of Language, 2017, London, pp.36-46. Dostupné z: https://www.aclweb.org/anthology/W17-3404/

Note:
Further information:
https://courses.fit.cvut.cz/MI-AVY
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2022-12-01
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet1433406.html