Automata that take advice

  • Carsten Damm
  • Markus Holzer
Contributed Papers Structural Complexity Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 969)


Karp and Lipton introduced advice-taking Turing machines to capture nonuniform complexity classes. We study this concept for automata-like models and compare it to other nonuniform models studied in connection with formal languages in the literature. Based on this we obtain complete separations of the classes of the Chomsky hierarchy relative to advices.


Turing Machine Regular Language Finite Automaton Kolmogorov Complexity Deterministic Finite Automaton 
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  1. 1.
    R. Aleliunas, R. M. Karp, R. J. Lipton, L. Lovasz, and C. Rackoff. Random walks, universal traversal sequences, and the complexity of MAZE problems. In Proceedings of the 20th IEEE Annual Symposium on Foundations of Computer Science, pages 218–223, 1979.Google Scholar
  2. 2.
    J. L. Balcázar, J. Díaz, and J. Gabarró. Uniform characterizations of non-uniform complexity measures. Information and Control, 67:53–69, 1985.Google Scholar
  3. 3.
    C. Damm and M. Holzer. Inductive counting below LOGSPACE. In Proceedings of the 19th Conference on Mathematical Foundations of Computer Science, number 841 in LNCS, pages 276–285. Springer, August 1994.Google Scholar
  4. 4.
    G. Goodrich, R. Ladner, and M. Fischer. Straight line programs to compute finite languages. In Conference on Theoretical Computer Science, Waterloo, 1977.Google Scholar
  5. 5.
    R. L. Graham, B. L. Rothschild, and J. H. Spencer. Ramsey theory. Wiley, 1990.Google Scholar
  6. 6.
    D. T. Huynh. Complexity of closeness, sparseness and segment equivalence for context-free and regular languages. In Informatik, Festschrift zum 60. Geburtstag von Günter Hotz, pages 235–251. B. G. Teubner, 1992.Google Scholar
  7. 7.
    O. H. Ibarra and B. Ravikumar. Sublogarithmic-space Turing machines, nonuniform space complexity, and closure properties. Mathematical Systems Theory, 21:1–17, 1988.Google Scholar
  8. 8.
    R. M. Karp and R. J. Lipton. Turing machines that take advice. L'Enseignement Mathématique, 28:191–209, 1982.Google Scholar
  9. 9.
    M. Li and P. Vitányi. An Introduction to Kolmogorov Complexity and its Applications. Springer, New York, Berlin, Heidelberg, 1993.Google Scholar
  10. 10.
    M. Mundhenk and R. Schuler. Random languages for nonuniform complexity classes. Journal of Complexity, 7:296–310, 1991.CrossRefGoogle Scholar
  11. 11.
    N. Pippenger. On simultaneous resource bounds. In Proceedings of the 20th IEEE Annual Symposium on Foundations of Computer Science, pages 307–311, 1979.Google Scholar
  12. 12.
    J. Shallit and Y. Breitbart. Automaticity: properties of a measure of descriptional complexity. In Annual Symposium on Theoretical Aspects of Computing, number 775 in Lecture Notes in Computer Science, pages 619–630. Springer, 1994.Google Scholar
  13. 13.
    A. Wigderson. NL/poly ⊂⊕L/poly. In Proceedings of the 9th Annual Structure in Complexity Theory Conference, pages 59–62, Juni 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Carsten Damm
    • 1
  • Markus Holzer
    • 2
  1. 1.FB IV-InformatikUniversität TrierTrierGermany
  2. 2.Wilhelm-Schickard-Institut für InformatikUniversität TübingenTübingenGermany

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