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Space bounded computations : Review and new separation results

  • J. Hartmanis
  • Desh Ranjan
Invited Lectures
Part of the Lecture Notes in Computer Science book series (LNCS, volume 379)

Abstract

In this paper we review the key results about space bounded complexity classes, discuss the central open problems and outline the relevant proof techniques. We show that, for a slightly modified Turing machine model, the low level deterministic and nondeterministic space bounded complexity classes are different. Furthermore, for this computation model, we show that Savitch and Immerman-Szelepcsényi theorems do not hold in the range lg lg n to lg n. We also discuss some other computation models to bring out and clarify the importance of space constructibility and establish some results about these models. We conclude by enumerating a few open problems which arise out of the discussion.

Keywords

Turing Machine Input Tape Deterministic Turing Machine Nondeterministic Turing Machine Work Tape 
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References

  1. [1]
    A.R. Freedman and R.E. Ladner. Space bounds for processing counterless inputs. Journal of Computer and System Sciences, 11:118–128, 1975.Google Scholar
  2. [2]
    R. Freivalds. On the worktime of deterministic and non-deterministic turing machines. Latvijskij Matematiceskij Eshegodnik, 23:158–165, 1979.Google Scholar
  3. [3]
    J. Hartmanis, R. Chang, J. Kadin, and S. Mitchell. Some observations about space bounded computations. Bulletin of the EATCS, 35:82–92, June 1988.Google Scholar
  4. [4]
    J. Hartmanis and H.H. Hunt. On the LBA problem and its importance in the theory of computation. SIAM-AMS, 7:1–26, 1974.Google Scholar
  5. [5]
    J.E. Hopcroft and J.D. Ullman. Introduction to Automats Theory, Languages and Computation. Addison-Wesley Publishing Company, 1979.Google Scholar
  6. [6]
    Neil Immerman. Nondeterministic space is closed under complement. In Proceedings of Structure in Complexity Theory Third Annual Conference, pages 112–115. Computer Society of IEEE, 1988.Google Scholar
  7. [7]
    S.Y. Kuroda. Classes of languages and linearly-bounded automata. Information and Control, 7:207–223, 1964.Google Scholar
  8. [8]
    P.M. Lewis II, R.E. Stearns, and J. Hartmanis. Memory bounds for recognition of context-free and context-sensitive languages. In IEEE Conference Record on Switching Circuit Theory and Logic Design, pages 191–202, 1965.Google Scholar
  9. [9]
    W.J. Savitch. Relationships between nondeterministic and deterministic tape complexities. Journal of Computer and System Sciences, 4:177–192, 1970.Google Scholar
  10. [10]
    Seiferas. A note on notions of tape constructibility. Technical Report CSD-TR 187, Pennsylvania State University, 1976.Google Scholar
  11. [11]
    M. Sipser. Halting space-bounded computations. Theoretical Computer Science, 10:335–338, 1980.Google Scholar
  12. [12]
    R.E. Stearns, J. Hartmanis, and P.M. Lewis II. Heirarchies of memory limited computations. In 1965 IEEE Conference Record on Switching Circuit Theory and Logical Design, pages 179–190, 1965.Google Scholar
  13. [13]
    R. Szelepcsényi. The method of forcing for nondeterministic automata. The Bulletin of the European Association for Theoretical Computer Science, 33:96–100, October 1987.Google Scholar
  14. [14]
    A. Szepietowski. Some notes on strong and weak log log n space complexity. Technical report, Mathematical Department, Technical University of Gda ńsk, Majakowskiego 11/12, PL-80-952 Gdańsk, Poland, 1988.Google Scholar
  15. [15]
    A. Szepietowski. If deterministic and nondeterministic space complexity are equal for log log n then they are equal for log n. In Lecture Notes in Computer Science, volume 349, pages 251–255. Springer-Verlag, 1989. STACS '89.Google Scholar
  16. [16]
    C.B. Wilson. Relativized circuit complexity. Journal of Computer and System Sciences, 31:169–181, 1985.Google Scholar
  17. [17]
    C.B. Wilson. Parallel computation and the NC heirarchy relativized. In Lecture Notes in Computer Science, volume 223, pages 362–382. Springer-Verlag, 1986. Structure in Complexity Theory.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • J. Hartmanis
    • 1
  • Desh Ranjan
    • 1
  1. 1.Computer Science DepartmentCornell UniversityUSA

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