Advertisement

Time and tape bounded auxiliary pushdown automata

  • I. H. Sudborough
Communications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 53)

Abstract

We consider language families defined by nondeterministic and deterministic log(n)-tape bounded auxiliary pushdown automata within polynomial time. It is known that these families are precisely the set of languages which are (many-one) log tape reducible to context-free languages and deterministic context-free languages, respectively. The results described here relate questions concerning these classes to other complexity classes and to questions concerning the tape complexity of context-free languages, resolution based proof procedures, solvable path systems, and deterministic context-free languages.

Keywords

Turing Machine Language Family Solution Graph Tree Resolution Path System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Sudborough, I.H., On the tape complexity of deterministic context-free languages, to appear in Journal of Assoc. for Comput. Mach. Google Scholar
  2. 2.
    Cook, S.A., Characterizations of pushdown machines in terms of time-bounded computers, Journal of Assoc. for Comput. Mach. 18 (1971), 4–18.Google Scholar
  3. 3.
    Jones, N.D., Space bounded reducibility among combinatorial problems, Journal of Comput. and System Sci. 11 (1975), 62–85.Google Scholar
  4. 4.
    Meyer, A.R. and L.J. Stockmeyer, Word problems requiring exponential time, in Proceedings of Fifth Annual Assoc. for Comput. Mach. Symposium on Theory of Computing (1973), 1–9. Association for Computing Machinery, 1133 Avenue of the Americas, New York.Google Scholar
  5. 5.
    Greibach, S.A., The hardest context-free language, SIAM Journal on Computing 2 (1973), 304–310.CrossRefGoogle Scholar
  6. 6.
    Sudborough, I.H., Separating tape bounded auxiliary pushdown automata classes, to appear in Proceedings of Ninth Annual Assoc. for Comput. Mach. Symposium on Theory of Computing (1977). (See reference 4 for address of ACM.)Google Scholar
  7. 7.
    Aho, A.V. and J.D. Ullman, The Theory of Parsing, Translation, and Compiling, vols. I and II, Prentice-Hall Publishing Co., Englewood Cliffs, New Jersey, U.S.A., 1972 and 1973.Google Scholar
  8. 8.
    Sudborough, I.H., The complexity of the membership problem for some extensions of context-free languages, to appear in International Journal of Computer Math. Google Scholar
  9. 9.
    Sudborough, I.H., The time and tape complexity of developmental languages, to appear in Proceedings of Fourth International Conference on Automata, Languages, and Programming, to be held in Turku, Finland (July 18–22, 1977). (The proceedings will be published in the Lecture Notes in Computer Science Series, Springer-Verlag Publishing Co., New York.)Google Scholar
  10. 10.
    Kasai, T., An hierarchy between context-free and context-sensitive languages, Journal of Computer and System Sci. 4 (1970), 492–508.Google Scholar
  11. 11.
    Cremers, A.B. and O. Mayer, On vector languages, Journal of Computer and System Sci. 8 (1974), 142–157.Google Scholar
  12. 12.
    Lewis, P.M., R.E. Stearns, and J. Hartmanis, Memory bounds for the recognition of context-free and context-sensitive languages, in Proceedings of the Sixth Annual IEEE Symposium on Switching Circuit Theory and Logical Design (1965), 199–212. (copies available from IEEE Computer Society, 5855 Naples Plaza, Suite 301, Long Beach, California, U.S.A.)Google Scholar
  13. 13.
    Cook, S.A., The complexity of theorem proving procedures, in Proceedings of the third Annual Assoc. for Comput. Mach. Symposium on Theory of Computing (1971), 151–158. (See reference 4 for address of ACM.)Google Scholar
  14. 14.
    Karp, R.M., Reducibilities among combinatorial problems, in Complexity of Computer Computation (R. Miller and J. Thatcher, Eds.), Plenum Publishing Company, New York, 1972.Google Scholar
  15. 15.
    Jones, N.D. and W.T. Laaser, Problems complete for deterministic polynomial time, to appear in Theoretical Computer Science. (A preliminary version appears in the Proceedings of the Sixth Annual ACM Symposium on Theory of Computing; see reference 4 for address information)Google Scholar
  16. 16.
    Cook, S.A., On observation on time-storage trade-off, Journal of Computer and System Sci. 9 (1974), 308–316.Google Scholar
  17. 17.
    Sudborough, I.H., On tape bounded complexity classes and multihead finite automata, Journal of Computer and System Sci. 10 (1975), 62–76.Google Scholar
  18. 18.
    Sudborough, I.H., On tape bounded complexity classes and linear context-free languages, Journal of Assoc. for Comput. Mach. 22 (1975), 500–501.Google Scholar
  19. 19.
    Jones, N.D., Y.E. Lien and W.T. Laaser, New problems complete for nondeterministic log space, Mathematical Systems Theory 10 (1976), 1–17.CrossRefGoogle Scholar
  20. 20.
    Cook, S.A., Path systems and language recognition, in Proceedings of Second Annual ACM Symposium on Theory of Computing (1970), 70–72. (See reference 4 for address information.)Google Scholar
  21. 21.
    Savitch, W.J., Relationships between nondeterministic and deterministic tape complexities, Journal of Computer and System Sci. 4 (1970), 177–192.Google Scholar
  22. 22.
    Ladner, R.E. and N.A. Lynch, Relativization of questions about log space computability, Mathematical Systems Theory 10 (1976), 19–32.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • I. H. Sudborough
    • 1
  1. 1.Department of Computer Science The Technological InstituteNorthwestern UniversityEvanstonUSA

Personalised recommendations