ON COMPLEXITY OF TOTAL DERIVABILITY PROBLEM IN NONCONTRACTING AND CONTEXT-FREE GRAMMARS
- Autores: Dudakov S.M1,2, Karlov B.N1
-
Afiliações:
- Tver State University
- National Research University «Higher School of Economics»
- Edição: Volume 524, Nº 1 (2025)
- Páginas: 11-18
- Seção: MATHEMATICS
- URL: https://pediatria.orscience.ru/2686-9543/article/view/691491
- DOI: https://doi.org/10.7868/S3034504925040024
- ID: 691491
Citar
Texto integral



Resumo
In this paper we study the problem of total derivability in context-free, noncontracting, and context-sensitive grammars. Given a grammar and a terminal word, one has to determine whether there exists a derivation of this word which uses each production no less than a given number of times. It is proved that the problem of total derivability of the emptyword in a context-free grammar is NP-complete. For noncontracting and context-sensitive grammars it is polynomially decidable for words of length 1, and it is NP-complete for every fixed word of length at least 2. Analagous results are obtained for another variant of the problem of total derivability when restrictions are placed on the amount of uses of nonterminals in the derivation.
Sobre autores
S. Dudakov
Tver State University; National Research University «Higher School of Economics»
Email: sergeydudakov@yandex.ru
Тверь, Россия; Москва, Россия
B. Karlov
Tver State University
Email: bnkarlov@gmail.com
Тверь, Россия
Bibliografia
- Shallit J. A second course in formal languages and automata theory. Cambridge: Cambridge University Press, 2008.
- Гэри М., Джонсон Д. Вычислительные машины и труднорешаемые задачи. М.: Мир, 1982.
- Valiant L.G. General context-free recognition in less than cubic time // J. Comput. Syst. Sci. 1975. V. 10. P. 308—315. https://doi.org/10.1016/S0022-0000(75)80046-8
- Дудаков С.М., Карлов Б.Н., Кузнецов С.Л., Фофанова Е.М. Сложность исчислений Ламбека с модальностями и тотальной выводимости в грамматиках // Алгебра и логика. 2021. Т. 60. № 5. С. 471—496. https://doi.org/10.33048/alglog.2021.60.502
- Event-Based Control and Signal Processing / ed. Miskowicz M. Boca Raton, FL: CRC Press, 2018. https://doi.org/10.1201/b19013
- Harrison M.A. Introduction to formal language theory. Reading, MA: Addison-Wesley, 1978.
- Ахо А., Хопкрофт Дж., Ульман Дж. Построение и анализ вычислительных алгоритмов. М.: Мир, 1979.
- Кормен Т.Х., Лейзерсон Ч.И., Ривест Р.Л., Штайн К. Алгоритмы: построение и анализ. 2–e изд. М.: Вильямс, 2011.
Arquivos suplementares
