Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Atcheson B., Ewert S., Shell D.: A note on the generative capacity of random context. S. Afr. Comput. J. 36, 95–98 (2006)
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)
Cremers A.B., Maurer H.A., Mayer O.: A note on leftmost restricted random context grammars. Inf. Process. Lett. 2(2), 31–33 (1973)
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)
Dassow J., Păun G.: Regulated Rewriting in Formal Language Theory. Springer, New York (1989)
Goldefus F., Masopust T., Meduna A.: Left-forbidding cooperating distributed grammar systems. Theor. Comput. Sci. 20(3), 1–11 (2010)
Greibach S.A., Hopcroft J.E.: Scattered context grammars. J. Comput. Syst. Sci. 3(3), 233–247 (1969)
Meduna A.: Automata and Languages: Theory and Applications. Springer, London (2000)
Meduna A., Techet J.: Scattered Context Grammars and their Applications. WIT Press, Southampton (2010)
Meduna A., Švec M.: Grammars with Context Conditions and Their Applications. Wiley, New Jersey (2005)
Penttonen M.: One-sided and two-sided context in formal grammars. Inf. Control 25(4), 371–392 (1974)
Păun G.: A variant of random context grammars: semi-conditional grammars. Theor. Comput. Sci. 41(1), 1–17 (1985)
Rozenberg, G., Salomaa, A. (eds): Handbook of Formal Languages. Linear Modeling: Background and Application chap. 3, vol. 2, pp. 101–154. Springer, Berlin (1997)
Salomaa A.: Formal Languages. Academic Press, London (1973)
van der Walt, A.P.J.: Random context grammars. In: Proceedings of Symposium on Formal Languages, pp. 163–165 (1970)
van der Walt A.P.J., Ewert S.: A shrinking lemma for random forbidding context languages. Theor. Comput. Sci. 237(1–2), 149–158 (2000)
van der Walt A.P.J., Ewert S.: A pumping lemma for random permitting context languages. Theor. Comput. Sci. 270(1–2), 959–967 (2002)
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)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Meduna, A., Zemek, P. One-sided random context grammars. Acta Informatica 48, 149–163 (2011). https://doi.org/10.1007/s00236-011-0134-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00236-011-0134-y