Skip to main content
SpringerLink
Log in

Probabilistic Length-Reducing Two-Pushdown Automata

  • Published:
Theory of Computing Systems Aims and scope Submit manuscript

Abstract

Hardness of a separation of nondeterminism, randomization and determinism for polynomial time computations has motivated the analysis of this issue for restricted models of computation. Following this line of research, we consider randomized length-reducing two-pushdown automata ( \(\mathsf{lrTPDA}\) ), a natural extension of pushdown automata ( \(\mathsf{PDA}\) ). Our main results are as follows. We show that deterministic \(\mathsf{lrTPDA}\) s are weaker than Las Vegas \(\mathsf{lrTPDA}\) s which in turn are weaker than Monte Carlo \(\mathsf{lrTPDA}\) s. Moreover, bounded two-sided error \(\mathsf{lrTPDA}\) s are stronger than Monte Carlo \(\mathsf{lrTPDA}\) s and they are able to recognize some languages which cannot be recognized nondeterministically. Finally, we prove that amplification is impossible for Las Vegas and Monte Carlo automata.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Buntrock, G., Loryś, K.: On growing context-sensitive languages. In: ICALP. Lecture Notes in Computer Science, vol. 623, pp. 77–88. Springer, Berlin (1992)

    Google Scholar 

  2. Buntrock, G., Otto, F.: Growing context-sensitive languages and Church–Rosser languages. Inf. Comput. 141(1), 1–36 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  3. Ďuriš, P., Hromkovič, J., Rolim, J.D.P., Schnitger, G.: Las Vegas versus determinism for one-way communication complexity, finite automata, and polynomial-time computations. In: STACS. Lecture Notes in Computer Science, vol. 1200, pp. 117–128. Springer, Berlin (1997)

    Google Scholar 

  4. Hromkovič, J., Schnitger, G.: On the power of randomized pushdown automata. In: Developments in Language Theory (DLT). Lecture Notes in Computer Science, vol. 2295, pp. 262–271. Springer, Berlin (2001)

    Chapter  Google Scholar 

  5. Hromkovič, J., Schnitger, G.: Pushdown automata and multicounter machines, a comparison of computation modes. In: ICALP. Lecture Notes in Computer Science, vol. 2719, pp. 66–80. Springer, Berlin (2003)

    Google Scholar 

  6. Hromkovič, J., Schnitger, G.: On the power of Las Vegas II: two-way finite automata. Theor. Comput. Sci. 262(1), 1–24 (2001)

    Article  MATH  Google Scholar 

  7. Dahlhaus, E., Warmuth, M.K.: Membership for growing context-sensitive grammars is polynomial. J. Comput. Syst. Sci. 33(3), 456–472 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  8. Jurdziński, T., Loryś, K.: Lower bound technique for length-reducing automata. Inf. Comput. 205(9), 387–1412 (2007)

    Google Scholar 

  9. Jurdziński, T.: Probabilistic length-reducing automata. In: MFCS. Lecture Notes in Computer Science, vol. 4162, pp. 561–572. Springer, Berlin (2006)

    Google Scholar 

  10. Kaneps, J., Geidmanis, D., Freivalds, R.: Tally languages accepted by Monte Carlo pushdown automata. In: RANDOM. Lecture Notes in Computer Science, vol. 1269, pp. 187–195. Springer, Berlin (1997)

    Google Scholar 

  11. Li, M., Vitanyi, P.: An Introduction to Kolmogorov Complexity and its Applications. Springer, Berlin (1993)

    MATH  Google Scholar 

  12. Macarie, I.I., Ogihara, M.: Properties of probabilistic pushdown automata. Theor. Comput. Sci. 207(1), 117–130 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  13. McNaughton, R.: An insertion into the Chomsky hierarchy? In: Karhumaki, J., Maurer, H.A., Paun, G., Rozenberg, G. (eds.) Jewels are Forever, Contributions on TCS in Honour of A. Salomaa, pp. 204–212. Springer, Berlin (1999)

    Google Scholar 

  14. McNaughton, R., Narendran, P., Otto, F.: Church–Rosser Thue systems and formal languages. J. Assoc. Comput. Mach. 35, 324–344 (1988)

    MATH  MathSciNet  Google Scholar 

  15. Niemann, G.: Church–Rosser languages and related classes. PhD thesis. Univ. Kassel (2002)

  16. Niemann, G., Otto, F.: The Church–Rosser languages are the deterministic variants of the growing context-sensitive languages. Inf. Comput. 197(1–2), 1–21 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  17. Sauerhoff, M.: Randomness versus nondeterminism for read-once and read-k branching programs. In: STACS 03. Lecture Notes in Computer Science, vol. 2607, pp. 307–318. Springer, Berlin (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Wrocław, Joliot-Curie 15, 50-383, Wrocław, Poland

    Tomasz Jurdziński

Authors
  1. Tomasz Jurdziński
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tomasz Jurdziński.

Additional information

Partially supported by MNiSW grant number N206 024 31/3826, 2006-2008. An extended abstract of this paper appeared in the MFCS06 Proceedings (Lecture Notes in Computer Science, vol. 4162, pp. 561–572, 2006).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jurdziński, T. Probabilistic Length-Reducing Two-Pushdown Automata. Theory Comput Syst 45, 74–107 (2009). https://doi.org/10.1007/s00224-007-9066-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00224-007-9066-x

Keywords

Search

Navigation