One-sided random context grammars
- 78 Downloads
The notion of a one-sided random context grammar is defined as a context-free-based regulated grammar, in which a set of permitting symbols and a set of forbidding symbols are attached to every rule, and its set of rules is divided into the set of left random context rules and the set of right random context rules. A left random context rule can rewrite a nonterminal if each of its permitting symbols occurs to the left of the rewritten symbol in the current sentential form while each of its forbidding symbols does not occur there. A right random context rule is applied analogically except that the symbols are examined to the right of the rewritten symbol. The paper demonstrates that without erasing rules, one-sided random context grammars characterize the family of context-sensitive languages, and with erasing rules, these grammars characterize the family of recursively enumerable languages. In fact, these characterization results hold even if the set of left random context rules coincides with the set of right random context rules. Several special cases of these grammars are considered, and their generative power is established. In its conclusion, some important open problems are suggested to study in the future.
KeywordsLanguage Family Sentential Form Formal Language Theory Context Grammar Context Language
Unable to display preview. Download preview PDF.
- 1.Atcheson B., Ewert S., Shell D.: A note on the generative capacity of random context. S. Afr. Comput. J. 36, 95–98 (2006)Google Scholar
- 2.Bordihn, H., Holzer, M.: Random context in regulated rewriting versus cooperating distributed grammar systems. In: LATA’08: Proceedings of the 2nd International Conference on Language and Automata Theory and Applications, pp. 125–136. Springer (2008)Google Scholar
- 4.Csuhaj-Varjú E., Masopust T., Vaszil G.: Cooperating distributed grammar systems with permitting grammars as components. Romanian J. Inf. Sci. Technol. 12(2), 175–189 (2009)Google Scholar
- 5.Dassow J., Păun G.: Regulated Rewriting in Formal Language Theory. Springer, New York (1989)Google Scholar
- 8.Meduna A.: Automata and Languages: Theory and Applications. Springer, London (2000)Google Scholar
- 13.Rozenberg, G., Salomaa, A. (eds): Handbook of Formal Languages. Linear Modeling: Background and Application chap. 3, vol. 2, pp. 101–154. Springer, Berlin (1997)Google Scholar
- 15.van der Walt, A.P.J.: Random context grammars. In: Proceedings of Symposium on Formal Languages, pp. 163–165 (1970)Google Scholar
- 18.Zetzsche, G.: On erasing productions in random context grammars. In: ICALP’10: Proceedings of the 37th International Colloquium on Automata, Languages and Programming, pp. 175–186. Springer (2010)Google Scholar