Speeding-up nondeterministic single-tape off-line computations by one alternation

Extended abstract
  • Jiří Wiedermann
Contributed Papers Turing Complexity and Logic
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1450)


It is shown that any nonderministic single-tape off-line Turing machine of time complexity T(n) can be speeded-up by one extra alternation by the factor log log T(n)/ √ log T(n), for any well-behaved function T(n). This leads to the separation NTIME1+I(T(n)) ⊂ σ 2 - TIME 1+I (T(n)) of the respective complexity classes. Analogous result holds also for the complementary classes co-NTIME1+I(T(n)) and π 2 - TIME1+I(T(n)). This is the first occasion where such separation results have been proved for a restricted type of multitape nondeterministic machines. For the general case of multitape nondeterministic machines similar results are not known to hold.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Book, R.V.-Greibach, S.A.-Wegbreit, B.: Time-and Tape-Bounded Turing Acceptors and AFLs. JCSS 4, Vol. 6, Dec. 1970, pp. 602–621Google Scholar
  2. 2.
    Hennie, F.C.: One-Tape, Off-line Turing Machine Computations. Information and Control, Vol. 8, 1965, pp. 553–578MathSciNetCrossRefGoogle Scholar
  3. 3.
    Dymond, P.W.-Tompa, M.: Speedups of Deterministic Machines by Synchronous Parallel Machines. In Proc. 24th Annual IEEE Symposium on Foundations of Computer Science, pp. 336–364, 1983Google Scholar
  4. 4.
    Gupta, S.: Alternating Time Versus Deterministic Time: A Separation. Proc. of Structure in Complexity, San Diego, 1993Google Scholar
  5. 5.
    Hopcroft, J.-Paul, W.-Valiant L.: On time versus space and related problems. Proc. IEEE FOCS 16, 1975, pp. 57–64MathSciNetGoogle Scholar
  6. 6.
    Kannan, R.: Alternation and the power of nondeterminism (Extended abstract). Proc. 15-th STOC, 1983, pp. 344–346Google Scholar
  7. 7.
    LoryŚ, K.-LiŚkiewicz, M.: Two Applications of Führers Counter to One-Tape Nondeterministic TMs. Proceedings of the MFCS'88, LNCS Vol. 324, Springer Verlag, 1988, pp. 445–453Google Scholar
  8. 8.
    Maass, W.: Combinatorial Lower Bound Arguments for Deterministic and Nondeterministic Turing Machines. Trans. Am. Math. Soc. 292, 1985, pp. 675–693MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Maass, W.-Schorr, A.: Speed-up of Turing Machines with One Work Tape and Two-way Input Tape. SIAM J. Comput., Vol. 16, no. 1, 1987, pp. 195–202MATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Paterson, M.: Tape Bounds for Time-Bounded Turing Machines, JCSS, Vol. 6, 1972, pp. 116–124MATHMathSciNetGoogle Scholar
  11. 11.
    Paul, W.-Prauss, E. J.-Reischuk, R.: On Alternation. Acta Informatica, 14, 1980, pp. 243–255MATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Paul, W.J.-Pippenger, N.-Szemerédi, E.-Trotter, W.T.: On determinism versus nondeterminism and related problems. In Proc. 24th Annual IEEE Symposium on Foundations of Computer Science, pp. 429–438, 1983Google Scholar
  13. 13.
    Wiedermann, J.: Speeding-up Single-Tape Nondeterministic Computations by Single Alternation, with Separation Results. Proceedings of the 23-rd International Colloquium on Automata, Languages, and Programming, ICALP'96, LNCS Vol. 1099, Springer Verlag, Berlin, 1996Google Scholar
  14. 14.
    Wiedermann, J.: Accelerating Nondeterministic Single-Tape Off-Line Computations by One Alternation. Technical Report V-725-97, Institute of Computer Science, Prague, 1998Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Jiří Wiedermann
    • 1
  1. 1.Institute of Computer ScienceAcademy of Sciences of the Czech RepublicPrague 8Czech Republic

Personalised recommendations