Probabilistic Length-Reducing Automata

  • Tomasz Jurdziński
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4162)


Hardness of a separation of nondeterminism, randomization and determinism for polynomial time computations motivates the analysis of restricted models of computation. Following this line of research, we consider randomized length-reducing two-pushdown automata (lrTPDA), a natural extension of pushdown automata (PDA). We separate randomized lrTPDAs from deterministic and nondeterministic ones, and we compare different modes of randomization. Moreover, we prove that amplification is impossible for Las Vegas automata.


Monte Carlo Transition Point Computation Graph Kolmogorov Complexity Short Sector 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Buntrock, G., Otto, F.: Growing Context-Sensitive Languages and Church-Rosser Languages. Information and Computation 141(1), 1–36 (1998)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Hromkovic, J., Schnitger, G.: Pushdown Automata and Multicounter Machines, a Comparison of Computation Modes. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 66–80. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  3. 3.
    Dahlhaus, E., Warmuth, M.K.: Membership for growing context-sensitive grammars is polynomial. Journal of Computer Systems Sciences 33(3), 456–472 (1986)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Jurdziński, T., Loryś, K.: Church-Rosser Languages vs. UCFL. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 147–158. Springer, Heidelberg (2002), CrossRefGoogle Scholar
  5. 5.
    Jurdziński, T.: The boolean closure of growing context-sensitive languages. In: H. Ibarra, O., Dang, Z. (eds.) DLT 2006. LNCS, vol. 4036, pp. 248–259. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Kaneps, J., Geidmanis, D., Freivalds, R.: Tally Languages Accepted by Monte Carlo Pushdown Automata. In: Rolim, J.D.P. (ed.) RANDOM 1997. LNCS, vol. 1269, pp. 187–195. Springer, Heidelberg (1997)Google Scholar
  7. 7.
    Li, M., Vitanyi, P.: An Introduction to Kolmogorov Complexity and its Applications. Springer, Heidelberg (1993)MATHGoogle Scholar
  8. 8.
    Macarie, I.I., Ogihara, M.: Properties of Probabilistic Pushdown Automata. Theor. Comput. Sci. 207(1), 117–130 (1998)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    McNaughton, R., Narendran, P., Otto, F.: Church-Rosser Thue systems and formal languages. Journal of the Association Computing Machinery 35, 324–344 (1988)MATHMathSciNetGoogle Scholar
  10. 10.
    Niemann, G.: Church-Rosser Languages and Related Classes, PhD Thesis, Univ. Kassel (2002)Google Scholar
  11. 11.
    Niemann, G., Otto, F.: The Church-Rosser languages are the deterministic variants of the growing context-sensitive languages. Inf. Comp. 197(1-2), 1–21 (2005)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Tomasz Jurdziński
    • 1
  1. 1.Institute of Computer ScienceWrocław UniversityWrocławPoland

Personalised recommendations