Skip to main content
SpringerLink
Log in

Transformational methods and their application to complexity problems

  • Published:
Acta Informatica Aims and scope Submit manuscript

Summary

The following results are proved by the use of transformabilities.

  1. 1.

    NTAPE (log n)=TAPE (log n)⇔There exists a j such that every language accepted by a nondeterministic one-way one-counter automaton is contained in D j. (D j is the family of all languages accepted by deterministic j-head two-way finite automata.)

  2. 2.

    NTAPE (n) =TAPE (n)⇔ There exists a j such that every language L ∉ {1}* accepted by a nondeterministic 5-head two-way finite automaton is contained in D j.

  3. 3.

    \(\mathop U\limits_d\) TIME (n d=TAPE (log n)⇔ There exists a j such that every language accepted by a deterministic 1-head two-way pushdown automaton is contained in D j.

  4. 4.

    f\(\mathop U\limits_d\) TIME (d n)=TAPE (n)⇔There exists a j such that every language L ⊂{1}* accepted by a deterministic 1-head two-way pushdown automaton is contained in D j.

  5. 5.

    D j ≨ D j+1 for all j ε εN.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Book, R. V.: On the structure of complexity classes. In: Nivat, M. (ed.): 2nd Colloquium on Automata, Languages and Programming 1974, p. 437–445

  2. Cook, S. A.: Characterizations of pushdown machines in terms of time bounded computers. J. ACM 18, 4–18 (1971)

    Article  MathSciNet  Google Scholar 

  3. Hartmanis, J.: On Non-determinacy in simple computing devices. Acta Informatica 1, 336–344 (1972)

    Article  Google Scholar 

  4. Ibarra, O. H.: On two-way multihead automata. J. Computer and System Sciences 7, 28–37 (1973)

    Article  MathSciNet  Google Scholar 

  5. Knuth, D. E.: Postscript about NP-hard problems. SIGACT News 6: 2, 15–16 (1974)

    Article  Google Scholar 

  6. Lewis, P. M., Stearns, R. E., Hartmanis, J.: Memory bounds for recognition of context-free and context-sensitive languages. IEEE Conf. Rec. 7-th Ann. Symp. Switch. Cir. Th. Log. Des. 1965, p. 191–202

  7. Monien, B.: Relationship between pushdown automata and tape—bounded Turing machines. 1st Colloquium on Automata, Languages and Programming 1972, p. 575–583

  8. Monien, B.: Characterizations of time-bounded computations by limited primitive recursion. 2nd Colloquium, Automata, Languages and Programming 1974, p. 280–293

  9. Savitch, W. J.: Relationships between nondeterministic and deterministic tape complexity. J. Computer and System Sciences 4, 177–192 (1970)

    Article  MathSciNet  Google Scholar 

  10. Savitch, W. J.: Maze recognizing automata and nondeterministic tape complexity. J. Computer and System Sciences 7, 389–403 (1973)

    Article  MathSciNet  Google Scholar 

  11. Savitch, W. J.: A note on multihead automata and context-sensitive languages. Acta Informatica 2, 249–252 (1973)

    Article  MathSciNet  Google Scholar 

  12. Sudborough, I. H.: On tape-bounded complexity classes and multi-head finite automata. IEEE Conf. Rec. 14-th Ann. Symp. Switch. Aut. Th. 1973, p. 138–144

Download references

Author information

Authors and Affiliations

  1. Universität Dortmund Abteilung Informatik, Postfach 500, D-4600, Dortmund-Hombruch, Deutschland

    Burkhard Monien

Authors
  1. Burkhard Monien
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Monien, B. Transformational methods and their application to complexity problems. Acta Informatica 6, 95–108 (1976). https://doi.org/10.1007/BF00263746

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00263746

Keywords

Search

Navigation