Project Details
Bezkontextové gramatiky a zásobníkové automaty
Project Period: 1. 1. 2010 – 31. 12. 2011
Project Type: grant
Code: MEB041003
Agency: Ministerstvo školství, mládeže a tělovýchovy ČR
Program: KONTAKT
formal language theory, primitive words, grammars, automata
The planned research will focus on the study of context-free languages and pushdown automata and their applications. To understand the structure of formal languages is a helpful tool to study their combinatorial properties. One of the subjects of this research is the problem of primitive words. A word is called primitive if it is not a power of another word. A widely known conjecture of P. Dömösi, M. Ito, and S. Horváth states that the language Q of all primitive words over an alphabet with several letters is not context-free. A number of recent papers investigated this well-known conjecture which is still open. We intend to continue our investigations on small context-free grammars generating primitive words. On the other hand, using the fact that a homomorphic map of a nonprimitive word is also nonprimitive, we also plan to study whether or not Q has a real Chomsky-Schützenberger-Stanley type homomorphic characterization. By our hope, these investigations may lead to prove or disprove our conjecture. In addition, we would like to characterize context-free languages consisting of non-primitive words. By this research we can also find new important properties of context-free languages. Studying the combinatorial properties of words and languages we can get a lot of information on the structure of languages in connection with the Chomsky hierarchy and corresponding automata. Regarding this subject, one of the most important results is the Bar-Hillel Lemma having an effective method for testing a language whether or not it is context-free. There are some well-known stronger versions of this result. One direction is to study the family of context-free non-linear languages. G. Horváth discovered a strong iteration property of context-free non-linear languages. In this project we would like to continue this line of research. By the well-known Chomsky-Schützenberger-Stanley theorem, every context-free language is homomorphically characterized by h and D, R, where h is a homomorphism, D is a Dyck language and R is a regular language. Several extensions of this result are known. In this project we plan to continue this research giving real homomorphic characterizations of context-free languages having certain combinatorial properties (slenderness, poly-slenderness, palindromicity, etc). The mathematical value of the expected results will be proved by their publications in international scientific journals and conferences.
Čermák Martin, Ing., Ph.D.
Koutný Jiří, Ing., Ph.D.
Křivka Zbyněk, Ing., Ph.D. (DIFS)
2012
- KOUTNÝ, J.; MEDUNA, A. Tree-controlled Grammars with Restrictions Placed upon Cuts and Paths. Kybernetika, 2012, vol. 48, no. 1,
p. 165-175. ISSN: 0023-5954. Detail - MEDUNA, A.; ČERMÁK, M.; HORÁČEK, P. Rule-restricted automaton-grammar transducers: Power and linguistic applications. Mathematics for applications, 2012, vol. 1, no. 1,
p. 13-35. ISSN: 1805-3610. Detail - MEDUNA, A.; ZEMEK, P. One-Sided Forbidding Grammars and Selective Substitution Grammars. International Journal of Computer Mathematics, 2012, vol. 89, no. 5,
p. 586-596. ISSN: 0020-7160. Detail
2011
- ČERMÁK, M.; KOUTNÝ, J.; MEDUNA, A. Parsing Based on n-Path Tree-Controlled Grammars. Theoretical and Applied Informatics, 2011, vol. 23, no. 3,
p. 213-228. ISSN: 1896-5334. Detail - ČERMÁK, M.; MEDUNA, A. n-Accepting Restricted Pushdown Automata Systems. 13th International Conference on Automata and Formal Languages. Nyíregyháza: Computer and Automation Research Institute, Hungarian Academy of Sciences, 2011.
p. 168-183. ISBN: 978-615-5097-19-5. Detail - KOUTNÝ, J.; KŘIVKA, Z.; MEDUNA, A. Pumping Properties of Path-Restricted Tree-Controlled Languages. 7th Doctoral Workshop on Mathematical and Engineering Methods in Computer Science. Brno: Brno University of Technology, 2011.
p. 61-69. ISBN: 978-80-214-4305-1. Detail - KŘIVKA, Z.; MASOPUST, T. Cooperating Distributed Grammar Systems with Random Context Grammars as Components. Acta Cybernetica, 2011, vol. 20, no. 2,
p. 269-283. ISSN: 0324-721X. Detail
2010
- LUKÁŠ, R.; MEDUNA, A. Multigenerative Grammar Systems and Matrix Grammars. Kybernetika, 2010, vol. 46, no. 1,
p. 68-82. ISSN: 0023-5954. Detail