Finite Automata with Advice Tapes

  • Uğur Küçük
  • A. C. Cem Say
  • Abuzer Yakaryılmaz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7907)


We define a model of advised computation by finite automata where the advice is provided on a separate tape. We consider several variants of the model where the advice is deterministic or randomized, the input tape head is allowed real-time, one-way, or two-way access, and the automaton is classical or quantum. We prove several separation results among these variants, and establish the relationships between this model and the previously studied ways of providing advice to finite automata.


advised computation finite automata random advice 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Karp, R., Lipton, R.: Turing machines that take advice. L’Enseignement Mathematique 28, 191–209 (1982)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Damm, C., Holzer, M.: Automata that take advice. In: Hájek, P., Wiedermann, J. (eds.) MFCS 1995. LNCS, vol. 969, pp. 149–158. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  3. 3.
    Tadaki, K., Yamakami, T., Lin, J.C.H.: Theory of one-tape linear-time Turing machines. Theoretical Computer Science 411(1), 22–43 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Dwork, C., Stockmeyer, L.: Finite state verifiers I: The power of interaction. Journal of the ACM 39(4), 800–828 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Freivalds, R.: Amount of nonconstructivity in deterministic finite automata. Theoretical Computer Science 411(38-39), 3436–3443 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Yamakami, T.: Swapping lemmas for regular and context-free languages with advice. Computing Research Repository abs/0808.4 (2008)Google Scholar
  7. 7.
    Yamakami, T.: The roles of advice to one-tape linear-time Turing machines and finite automata. Int. J. Found. Comput. Sci. 21(6), 941–962 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Yamakami, T.: Immunity and pseudorandomness of context-free languages. Theoretical Computer Science 412(45), 6432–6450 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Yamakami, T.: One-way reversible and quantum finite automata with advice. In: Dediu, A.-H., Martín-Vide, C. (eds.) LATA 2012. LNCS, vol. 7183, pp. 526–537. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  10. 10.
    Agadzanyan, R., Freivalds, R.: Finite state transducers with intuition. In: Calude, C.S., Hagiya, M., Morita, K., Rozenberg, G., Timmis, J. (eds.) Unconventional Computation. LNCS, vol. 6079, pp. 11–20. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Goldreich, O.: Computational Complexity: A Conceptual Perspective. Cambridge University Press (2008)Google Scholar
  12. 12.
    Yakaryılmaz, A., Say, A.C.C.: Unbounded-error quantum computation with small space bounds. Information and Computation 279(6), 873–892 (2011)CrossRefGoogle Scholar
  13. 13.
    Hirvensalo, M.: Quantum automata with open time evolution. International Journal of Natural Computing Research 1(1), 70–85 (2010)CrossRefGoogle Scholar
  14. 14.
    Kondacs, A., Watrous, J.: On the power of quantum finite state automata. In: Proceedings of the 38th Annual Symposium on Foundations of Computer Science, FOCS 1997, pp. 66–75 (1997)Google Scholar
  15. 15.
    Shepherdson, J.C.: The reduction of two–way automata to one-way automata. IBM Journal of Research and Development 3, 198–200 (1959)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Freivalds, R.: Fast probabilistic algorithms. In: Becvar, J. (ed.) MFCS 1979. LNCS, vol. 74, pp. 57–69. Springer, Heidelberg (1979)CrossRefGoogle Scholar
  17. 17.
    Yakaryilmaz, A., Freivalds, R., Say, A.C.C., Agadzanyan, R.: Quantum computation with write-only memory. Natural Computing 11(1), 81–94 (2012)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Uğur Küçük
    • 1
  • A. C. Cem Say
    • 1
  • Abuzer Yakaryılmaz
    • 2
  1. 1.Boğaziçi UniversityIstanbulTurkey
  2. 2.University of LatviaRīgaLatvia

Personalised recommendations