Deciding verbose languages with linear advice

  • Arfst Nickelsen
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1295)


A language A is verbose if for some k there is a Turing machine M that for every input of k words w, ... , wk computes a bitstring of length k that is not the characteristic string X A (w1, ... , wk). A language A is p-verbose (or A ∈ P-verb) if M is polynomially time bounded. Linear advice is sufficient to decide p-verbose languages in linear exponential time. Even languages that are linear-exponential time Turing reducible with linearly many queries to a p-verbose language are in E/lin. In [BL97] the special case of Turing reductions with a bounded number of queries to a p-selective language was investigated. Their results are extended to the general case of bounded Turing reductions to p-verbose languages.

In particular, it is shown that Elin-T(P-verb) ⊂ E/lin; and EXP/poly is characterized as EXP poly-T (P-verb). On the other hand for fixed c and k it holds that E\(\nsubseteq\)P cn-T (P-k-verb) and \(EXP \nsubseteq E_{n^c } \left( { \nsubseteq - k - verb} \right)\).


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [ABG90]
    A. Amir, R. Beigel, and W. Gasarch. Some connections between bounded query classes and non uniform complexity. In Proc. 5th Structure in Complexity Theory, 1990.Google Scholar
  2. [BDG88]
    J. Balcázar, J. Diaz, and J. Gabarró. Structural Complexity I. Springer, 1988.Google Scholar
  3. [BKS94]
    R. Beigel, M. Kummer, and F. Stephan. Approximable sets. In Proc. 9th Structure in Complexity Theory, 1994.Google Scholar
  4. [BL97]
    H. J. Burtschick and W. Lindner. On sets turing reducible to p-selective sets. Theory of Computing Systems (formerly MST), 30:135–143, 1997.CrossRefGoogle Scholar
  5. [HT96]
    L. Hemaspaandra and T. Torenvliet. Optimal advice. Theoretical Computer Science, 154:367–377, 1996.CrossRefGoogle Scholar
  6. [Ko83]
    K.-I. Ko. On self-reducibility and weak p-selectivity. Trans. Amer. Math. Soc., 131:420–436, 1983.Google Scholar
  7. [Nic97]
    A. Nickelsen. On polynomially d-verbose sets. In Proc. STACS 97, 1997.Google Scholar
  8. [Sel79]
    A. Selman. P-selective sets, tally languages and the behaviour of polynomial time reducibilities on np. Mathematical Systems Theory, 13:55–65, 1979.CrossRefGoogle Scholar
  9. [Sel82]
    A. Selman. Analogues of semirecursive sets and effective reducibilities to the study of NP complexity. Information and Control, 1, 1982.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Arfst Nickelsen
    • 1
  1. 1.Fachbereich InformatikTechnische Universität BerlinBerlinGermany

Personalised recommendations