Advertisement

On the Complexity of 2-Monotone Restarting Automata

  • T. Jurdziński
  • F. Otto
  • F. Mráz
  • M. Plátek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3340)

Abstract

The R-automaton is the weakest form of the restarting automaton. It is shown that the class of languages accepted by these automata is incomparable under set inclusion to the class of growing context-sensitive languages. In fact, this already holds for the class of languages that are accepted by 2-monotone R-automata. Further it is shown that already this class contains NP -complete languages. Thus, already the 2-monotone R-automaton has a surprisingly large expressive power.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Buntrock, G.: Wachsende kontext-sensitive Sprachen. Habilitationsschrift, Fakultät für Mathematik und Informatik, Universität Würzburg (1996)Google Scholar
  2. 2.
    Buntrock, G., Otto, F.: Growing context-sensitive languages and Church-Rosser languages. Inform. and Comput. 141, 1–36 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Dahlhaus, E., Warmuth, M.: Membership for growing context-sensitive grammars is polynomial. J. Comput. System Sci. 33, 456–472 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Jančar, P., Mráz, F., Plátek, M., Vogel, J.: Restarting automata. In: Reichel, H. (ed.) FCT 1995. LNCS, vol. 965, pp. 283–292. Springer, Heidelberg (1995)Google Scholar
  5. 5.
    Jančar, P., Mráz, F., Plátek, M., Vogel, J.: On monotonic automata with a restart operation. J. Autom. Lang. Comb. 4, 287–311 (1999)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Jurdziński, T., Loryś, K., Niemann, G., Otto, F.: Some Results on RRW- and RRWW-Automata and Their Relationship to the Class of Growing Context-Sensitive Languages. Mathematische Schriften Kassel 14 (2001); Also: J. Autom. Lang. Comb., (to appear)Google Scholar
  7. 7.
    Jurdziński, T., Otto, F., Mráz, F., Plátek, M.: On the Complexity of 2-Monotone Restarting Automata. Mathematische Schriften Kassel, no. 4/04 (2004), Available at http://www.theory.informatik.uni-kassel.de/techreps/TR-2004-4.ps
  8. 8.
    Lautemann, C.: One pushdown and a small tape. In: Wagner, K.W. (ed.) Dirk Siefkes zum 50. Geburtstag, Technische Universität Berlin and Universität Augsburg, pp. 42–47 (1988)Google Scholar
  9. 9.
    McNaughton, R., Narendran, P., Otto, F.: Church-Rosser Thue systems and formal languages. J. Assoc. Comput. Mach. 35, 324–344 (1988)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Niemann, G., Otto, F.: The Church-Rosser languages are the deterministic variants of the growing context-sensitive languages. In: Nivat, M. (ed.) FOSSACS 1998. LNCS, vol. 1378, pp. 243–257. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  11. 11.
    Niemann, G., Otto, F.: Restarting automata, Church-Rosser languages, and representations of r.e. languages. In: Rozenberg, G., Thomas, W. (eds.) Proc. of DLT 1999, pp. 103–114. World Scientific, Singapore (2000)Google Scholar
  12. 12.
    Niemann, G., Otto, F.: Further results on restarting automata. In: Ito, M., Imaoka, T. (eds.) Proc. Words, Languages and Combinatorics III, pp. 352–369. World Scientific, Singapore (2003)CrossRefGoogle Scholar
  13. 13.
    Otto, F.: Restarting automata and their relations to the Chomsky hierarchy. In: Ésik, Z., Fülöp, Z. (eds.) DLT 2003. LNCS, vol. 2710, pp. 55–74. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  14. 14.
    Plátek, M.: Two-way restarting automata and j-monotonicity. In: Pacholski, L., Ružička, P. (eds.) SOFSEM 2001. LNCS, vol. 2234, pp. 316–325. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  15. 15.
    Plátek, M., Mráz, F.: Degrees of (non)monotonicity of RRW-automata. In: Dassow, J., Wotschke, D. (eds.) Preproceedings of the 3rd Workshop on Descriptional Complexity of Automata, Grammars and Related Structures, Report No. 16, pp. 159–165. Fakultät für Informatik, Universität Magdeburg (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • T. Jurdziński
    • 1
  • F. Otto
    • 1
  • F. Mráz
    • 2
  • M. Plátek
    • 2
  1. 1.Fachbereich Mathematik/InformatikUniversität KasselKasselGermany
  2. 2.Department of Computer ScienceCharles UniversityPragueCzech Republic

Personalised recommendations