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One-Sided Random Context Grammars with Leftmost Derivations

  • Alexander Meduna
  • Petr Zemek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7300)

Abstract

In this paper, we study the generative power of one-sided random context grammars working in a leftmost way. More specifically, by analogy with the three well-known types of leftmost derivations in regulated grammars, we introduce three types of leftmost derivations to one-sided random context grammars and prove the following three results. (I) One-sided random context grammars with type-1 leftmost derivations characterize the family of context-free languages. (II) One-sided random context grammars with type-2 and type-3 leftmost derivations characterize the family of recursively enumerable languages. (III) Propagating one-sided random context grammars with type-2 and type-3 leftmost derivations characterize the family of context-sensitive languages. In the conclusion, the generative power of random context grammars and one-sided random context grammars with leftmost derivations is compared.

Keywords

formal languages regulated rewriting one-sided random context grammars leftmost derivations generative power 

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References

  1. 1.
    Aho, A.V., Lam, M.S., Sethi, R., Ullman, J.D.: Compilers: Principles, Techniques, and Tools, 2nd edn. Addison-Wesley, Boston (2006)zbMATHGoogle Scholar
  2. 2.
    Aho, A.V., Ullman, J.D.: The Theory of Parsing, Translation and Compiling. Parsing, vol. I. Prentice-Hall, New Jersey (1972)zbMATHGoogle Scholar
  3. 3.
    Baker, B.S.: Non-context-free grammars generating context-free languages. Information and Control 24(3), 231–246 (1974)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Cannon, R.L.: Phrase structure grammars generating context-free languages. Information and Control 29(3), 252–267 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Cojocaru, L., Mäkinen, E.: On the complexity of Szilard languages of regulated grammars. Tech. rep., Department of Computer Sciences, University of Tampere, Tampere, Finland (2010)Google Scholar
  6. 6.
    Cremers, A.B., Maurer, H.A., Mayer, O.: A note on leftmost restricted random context grammars. Information Processing Letters 2(2), 31–33 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Cytron, R., Fischer, C., LeBlanc, R.: Crafting a Compiler. Addison-Wesley, Boston (2009)Google Scholar
  8. 8.
    Dassow, J., Fernau, H., Păun, G.: On the leftmost derivation in matrix grammars. International Journal of Foundations of Computer Science 10(1), 61–80 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Dassow, J., Păun, G.: Regulated Rewriting in Formal Language Theory. Springer, New York (1989)CrossRefzbMATHGoogle Scholar
  10. 10.
    Fernau, H.: Regulated grammars under leftmost derivation. Grammars 3(1), 37–62 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Fernau, H.: Nonterminal complexity of programmed grammars. Theoretical Computer Science 296(2), 225–251 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Ferretti, C., Mauri, G., Păun, G., Zandron, C.: On three variants of rewriting P systems. Theoretical Computer Science 301(1-3), 201–215 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Freund, R., Oswald, M.: P Systems with Activated/Prohibited Membrane Channels. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2002. LNCS, vol. 2597, pp. 261–269. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  14. 14.
    Ginsburg, S., Spanier, E.H.: Control sets on grammars. Theory of Computing Systems 2(2), 159–177 (1968)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Kasai, T.: An hierarchy between context-free and context-sensitive languages. Journal of Computer and System Sciences 4, 492–508 (1970)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Lukáš, R., Meduna, A.: Multigenerative grammar systems. Schedae Informaticae 2006(15), 175–188 (2006)zbMATHGoogle Scholar
  17. 17.
    Luker, M.: A generalization of leftmost derivations. Theory of Computing Systems 11(1), 317–325 (1977)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Matthews, G.H.: A note on asymmetry in phrase structure grammars. Information and Control 7, 360–365 (1964)CrossRefzbMATHGoogle Scholar
  19. 19.
    Maurer, H.: Simple matrix languages with a leftmost restriction. Information and Control 23(2), 128–139 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Meduna, A.: On the Number of Nonterminals in Matrix Grammars with Leftmost Derivations. In: Păun, G., Salomaa, A. (eds.) New Trends in Formal Languages. LNCS, vol. 1218, pp. 27–38. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  21. 21.
    Meduna, A.: Elements of Compiler Design. Auerbach Publications, Boston (2007)zbMATHGoogle Scholar
  22. 22.
    Meduna, A., Goldefus, F.: Weak leftmost derivations in cooperative distributed grammar systems. In: MEMICS 2009: 5th Doctoral Workshop on Mathematical and Engineering Methods in Computer Science, pp. 144–151. Brno University of Technology, Brno (2009)Google Scholar
  23. 23.
    Meduna, A., Techet, J.: Canonical scattered context generators of sentences with their parses. Theoretical Computer Science 2007(389), 73–81 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Meduna, A., Techet, J.: Scattered Context Grammars and their Applications. WIT Press, Southampton (2010)zbMATHGoogle Scholar
  25. 25.
    Meduna, A., Škrkal, O.: Combined leftmost derivations in matrix grammars. In: ISIM 2004: Proceedings of 7th International Conference on Information Systems Implementation and Modelling, Ostrava, CZ, pp. 127–132 (2004)Google Scholar
  26. 26.
    Meduna, A., Zemek, P.: Nonterminal complexity of one-sided random context grammars. Acta Informatica 49(2), 55–68 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Meduna, A., Zemek, P.: One-sided random context grammars. Acta Informatica 48(3), 149–163 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Mihalache, V.: Matrix grammars versus parallel communicating grammar systems. In: Mathematical Aspects of Natural and Formal Languages, pp. 293–318. World Scientific Publishing, River Edge (1994)CrossRefGoogle Scholar
  29. 29.
    Mutyam, M., Krithivasan, K.: Tissue P systems with leftmost derivation. Ramanujan Mathematical Society Lecture Notes Series 3, 187–196 (2007)MathSciNetzbMATHGoogle Scholar
  30. 30.
    Păun, G.: On leftmost derivation restriction in regulated rewriting. Romanian Journal of Pure and Applied Mathematics 30(9), 751–758 (1985)MathSciNetzbMATHGoogle Scholar
  31. 31.
    Rosenkrantz, D.J.: Programmed grammars and classes of formal languages. Journal of the ACM 16(1), 107–131 (1969)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, vol. 1 through 3. Springer, Berlin (1997)Google Scholar
  33. 33.
    Salomaa, A.: Matrix grammars with a leftmost restriction. Information and Control 20(2), 143–149 (1972)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Alexander Meduna
    • 1
  • Petr Zemek
    • 1
  1. 1.Faculty of Information Technology, IT4Innovations Centre of ExcellenceBrno University of TechnologyBrnoCzech Republic

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