Advertisement

Finite State Verifiers with Constant Randomness

  • A. C. Cem Say
  • Abuzer Yakaryılmaz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7318)

Abstract

We give a new characterization of NL as the class of languages whose members have certificates that can be verified with small error in polynomial time by finite state machines that use a constant number of random bits, as opposed to its conventional description in terms of deterministic logarithmic-space verifiers. It turns out that allowing two-way interaction with the prover does not change the class of verifiable languages, and that no polynomially bounded amount of randomness is useful for constant-memory computers when used as language recognizers, or public-coin verifiers.

Keywords

Regular Language Input String Input Tape Nondeterministic Choice Probabilistic Automaton 
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.
    Condon, A.: Computational Models of Games. MIT Press (1989)Google Scholar
  2. 2.
    Condon, A.: Space-bounded probabilistic game automata. Journal of the ACM 38(2), 472–494 (1991)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Condon, A.: The complexity of the max word problem and the power of one-way interactive proof systems. Computational Complexity 3(3), 292–305 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Condon, A.: The complexity of space bounded interactive proof systems. In: Complexity Theory: Current Research, pp. 147–190. Cambridge University Press (1993)Google Scholar
  5. 5.
    Condon, A., Ladner, R.: Interactive proof systems with polynomially bounded strategies. Journal of Computer and System Sciences 50(3), 506–518 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Condon, A., Lipton, R.J.: On the complexity of space bounded interactive proofs. In: Proceedings of the 30th Annual Symposium on Foundations of Computer Science. pp. 462–467 (1989), http://portal.acm.org/citation.cfm?id=1398514.1398732
  7. 7.
    Dwork, C., Stockmeyer, L.: A time complexity gap for two-way probabilistic finite-state automata. SIAM Journal on Computing 19(6), 1011–1123 (1990)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Dwork, C., Stockmeyer, L.: Finite state verifiers I: The power of interaction. Journal of the ACM 39(4), 800–828 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Freivalds, R.: Probabilistic two-way machines. In: Proceedings of the International Symposium on Mathematical Foundations of Computer Science, pp. 33–45 (1981)Google Scholar
  10. 10.
    Goldwasser, S., Sipser, M.: Private coins versus public coins in interactive proof systems. In: Proceedings of the 18th Annual ACM Symposium on Theory of Computing (STOC 1986), pp. 59–68 (1986)Google Scholar
  11. 11.
    Hartmanis, J.: On non-determinancy in simple computing devices. Acta Informatica 1, 336–344 (1972)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Holzer, M., Kutrib, M., Malcher, A.: Complexity of multi-head finite automata: Origins and directions. Theoretical Computer Science 412, 83–96 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Kaņeps, J.: Stochasticity of the languages acceptable by two-way finite probabilistic automata. Diskretnaya Matematika 1, 63–67 (1989) (Russian)Google Scholar
  14. 14.
    Kaņeps, J., Freivalds, R.: Running Time to Recognize Nonregular Languages by 2-Way Probabilistic Automata. In: Leach Albert, J., Monien, B., Rodríguez-Artalejo, M. (eds.) ICALP 1991. LNCS, vol. 510, pp. 174–185. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  15. 15.
    Macarie, I.I.: Space-efficient deterministic simulation of probabilistic automata. SIAM Journal on Computing 27(2), 448–465 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Shamir, A.: IP = PSPACE. Journal of the ACM 39(4), 869–877 (1992)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • A. C. Cem Say
    • 1
  • Abuzer Yakaryılmaz
    • 2
  1. 1.Department of Computer EngineeringBoğaziçi UniversityBebekTurkey
  2. 2.Faculty of ComputingUniversity of LatviaRīgaLatvia

Personalised recommendations