Advertisement

Acta Informatica

, Volume 48, Issue 3, pp 149–163 | Cite as

One-sided random context grammars

  • Alexander Meduna
  • Petr Zemek
Original Article

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.

Keywords

Language Family Sentential Form Formal Language Theory Context Grammar Context Language 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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. 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
  3. 3.
    Cremers A.B., Maurer H.A., Mayer O.: A note on leftmost restricted random context grammars. Inf. Process. Lett. 2(2), 31–33 (1973)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 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. 5.
    Dassow J., Păun G.: Regulated Rewriting in Formal Language Theory. Springer, New York (1989)Google Scholar
  6. 6.
    Goldefus F., Masopust T., Meduna A.: Left-forbidding cooperating distributed grammar systems. Theor. Comput. Sci. 20(3), 1–11 (2010)MathSciNetGoogle Scholar
  7. 7.
    Greibach S.A., Hopcroft J.E.: Scattered context grammars. J. Comput. Syst. Sci. 3(3), 233–247 (1969)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Meduna A.: Automata and Languages: Theory and Applications. Springer, London (2000)Google Scholar
  9. 9.
    Meduna A., Techet J.: Scattered Context Grammars and their Applications. WIT Press, Southampton (2010)zbMATHGoogle Scholar
  10. 10.
    Meduna A., Švec M.: Grammars with Context Conditions and Their Applications. Wiley, New Jersey (2005)CrossRefzbMATHGoogle Scholar
  11. 11.
    Penttonen M.: One-sided and two-sided context in formal grammars. Inf. Control 25(4), 371–392 (1974)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Păun G.: A variant of random context grammars: semi-conditional grammars. Theor. Comput. Sci. 41(1), 1–17 (1985)CrossRefzbMATHGoogle Scholar
  13. 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
  14. 14.
    Salomaa A.: Formal Languages. Academic Press, London (1973)zbMATHGoogle Scholar
  15. 15.
    van der Walt, A.P.J.: Random context grammars. In: Proceedings of Symposium on Formal Languages, pp. 163–165 (1970)Google Scholar
  16. 16.
    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)CrossRefzbMATHGoogle Scholar
  17. 17.
    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)zbMATHGoogle Scholar
  18. 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

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of Information Systems, Faculty of Information TechnologyBrno University of TechnologyBrnoCzech Republic

Personalised recommendations