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New developments in structural complexity theory

  • J. Hartmanis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 317)

Abstract

This paper discusses the scope and goals of structural complexity theory, describes some working hypothesis of this field and summarizes (some) recent developments.

Keywords

Complexity Class Input Tape Polynomial Hierarchy Polynomial Time Hierarchy Work Tape 
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.

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References

  1. [Be]
    Beigel, R. “Bounded Queries to SAT and the Boolean Hierarchy”, manuscript, June 1987.Google Scholar
  2. [BGS]
    Baker, T., J. Gill, and R. Solovay. “Relativizations of the P =? NP Question”, SIAM Journal on Computing, 4(4):431–442, December 1975.Google Scholar
  3. [BH]
    Berman, L. and J. Hartmanis. “On Isomorphisms and Density of NP and Other Complete Sets”, SIAM Journal on Computing, 6(2):305–322, June 1977.Google Scholar
  4. [CH1]
    Cai, J. and L. Hemachandra. “The Boolean Hierarchy: Hardware Over NP”, Technical Report, TR 85-724, Cornell Department of Computer Science, December 1985.Google Scholar
  5. [CH2]
    Cai, J. and L. Hemachandra. “The Boolean Hierarchy: Hardware Over NP”, Structure in Complexity Theory, pp. 105–124, Springer-Verlag Lecture Notes in Computer Science, No. 223, 1986.Google Scholar
  6. [GJ]
    Goldsmith, J. and D. Joseph. “Three Results on the Polynomial Isomorphism of Complete Sets”, Proceedings IEEE Symposium on Foundations of Computer Science, pp. 390–397, 1986.Google Scholar
  7. [Ha1]
    Hartmanis, J. “The Structural Complexity Column: A Retrospective on Structural Complexity”, EATCS Bulletin, 31:115, February 1987.Google Scholar
  8. [Ha2]
    Hartmanis, J. “The Structural Complexity Column: Sparse Complete Sets for NP and the Optimal Collapse of the Polynomial Hierarchy”, EATCS Bulletin, 32:73–81, June 1987.Google Scholar
  9. [Ha3]
    Hartmanis, J. “The Structural Complexity Column: The Collapsing Hierarchies”, EATCS Bulletin, 33:26–39, October 1987.Google Scholar
  10. [Ha4]
    Hartmanis, J. “Solvable Problems with Conflicting Relativizations”, EATCS Bulletin, 27:40–49, October 1985.Google Scholar
  11. [Ha5]
    Hartmanis, J. “Some Observations about NP Complete Sets”, Fundamentals of Computational Theory, Springer-Verlag Lecture Notes in Computer Science, 278:185–196, 1987.Google Scholar
  12. [Ha6]
    Hartmanis, J. “Generalized Kolmogorov Complexity and the Structure of Feasible Computations”, Proceedings 24th Annual Symposium on Foundations of Computer Science, IEEE Computer Society, 439–445.Google Scholar
  13. [He]
    Hemachandra, L. “The Strong Exponential Hierarchy Collapses”, ACM Symposium of Theory of Computing, pp. 110-122, 1987.Google Scholar
  14. [HIS]
    Hartmanis, J., N. Immerman, and V. Sewelson. “Sparse Sets in NP — P:EXPTIME Versus NEXPTIME”, Information and Control, 65:159–181, May/June 1985.Google Scholar
  15. [Ho]
    Hopcroft, J.E. “Turing Machines”, Scientific American, pp. 86–98, May 1984.Google Scholar
  16. [HU]
    Hopcroft, J. and J. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, 1979.Google Scholar
  17. [HY]
    Hartmanis, J. and Y. Yesha. “Computation Times of NP Sets of Different Densities”, Theoretical Computer Science, 34:17–32, 1984.Google Scholar
  18. [Imm]
    Immerman, N. “Nondeterministic Space is Closed Under Complement”, Yale University Technical Report, August 1987 (accepted for publication in SICOMP).Google Scholar
  19. [Ka1]
    Kadin, J. “P NP[logn] and Sparse Turing Complete Sets for NP”, Proceedings 2nd Structure in Complexity Theory Conference, pp. 33–40, Ithaca, New York, June 1987. Submitted to Journal of Computer and Systems Sciences.Google Scholar
  20. [Ka2]
    Kadin, J. Restricted Turing Reducibilities and the Structure of the Polynomial Time Hierarchy. Ph.D. Thesis, Cornell University, February 1988.Google Scholar
  21. [Ka3]
    Kadin, J. “The Polynomial Hierarchy Collapses if the Boolean Hierarchy Collapses”, Cornell University, Department of Computer Science Technical Report, TR 87-843, June 1987.Google Scholar
  22. [KiLa]
    Kirsig, B. and K. J. Lange. “Separation with the Ruzzo, Simon, and Tompa Relativization Implies DSPACE[logn] ≠ NSPACE[logn]” Information Processing Letters, 25:13–15, 1987.Google Scholar
  23. [KL]
    Karp, R. and R. Lipton, “Some Connections Between Nonuniform and Uniform Complexity Classes”, ACM Symposium on Theory of Computing, pp. 302–309, 1980.Google Scholar
  24. [KMR]
    Kurtz, S., S. Mahaney, and J. Royer. “Collapsing Degrees.” Proceedings IEEE Symposium on Foundations of Computer Science, pp. 380–389, 1986.Google Scholar
  25. [LKJ]
    Lange, K., B. Jenner, and B. Kirsig. “The Logarithmic Alternation Hierarchy Collapses: A Σ2L=A Π2L”, Automata, Languages, and Programming (ICALP 1987), Springer-Verlag Lecture Notes in Computer Science, 267:529–541, 1987.Google Scholar
  26. [Lo]
    Long, T. “A Note on Sparse Oracles for NP”, Journal of Computer and System Sciences, 24:224–232, 1982.Google Scholar
  27. [LL]
    Ladner, R. E. and N. A. Lynch. “Relativization of Questions About Log Space Computability.” Mathematical Systems Theory, 10:19–32, 1976.Google Scholar
  28. [Ma1]
    Mahaney, S. “Sparse Complete Sets for NP: Solution of a Conjecture of Berman and Hartmanis”, Journal of Computer and System Sciences, 25(2)130–143, 1982.Google Scholar
  29. [Ma2]
    Mahaney, S. “Sparse Sets and Reducibilities.” Studies in Complexity Theory, ed. R.V. Book, John Wiley and Sons, Inc. New York, pp. 63–118, 1986.Google Scholar
  30. [Mah]
    Mahaney S., ed. Proceedings Structure in Complexity Theory, Second Annual Conference Computer Society Press, 1987.Google Scholar
  31. [MY]
    Mahaney, S. and P. Young. “Reductions Among Polynomial Isomorphism Types”, Theoretical Computer Science, 207–224, 1985.Google Scholar
  32. [RS]
    Rackoff, C.W. and J. I. Seiferas. “Limitations on Separating Nondeterministic Complexity Classes”, SIAM Journal on Computing, 10:742–745, 1981.Google Scholar
  33. [RST]
    Ruzzo, W.L., J. Simon, and M. Tompa. “Space-Bounded Hierarchies and Probabilistic Computations”, Journal of Computer and Systems Sciences, 28(4):216–230, November 1984.Google Scholar
  34. [Sa]
    Savitch, W.J. “Relationships Between Nondeterministic and Deterministic Tape Complexities”, Journal of Computer and Systems Sciences, 4(2):177–192, 1970Google Scholar
  35. [Se]
    Selman, A.L., ed. Proceedings Structure in Complexity Theory, Springer Verlag Lecture Notes in Computer Science, No. 223, 1986.Google Scholar
  36. [Si]
    Simon, I. On Some Subrecursive Reducibilities. Ph.D. Thesis, Stanford University, March 1977.Google Scholar
  37. [St-]
    Stockmeyer, L. “The Polynomial-Time Hierarchy”, Theoretical Computer Science, 3:1–22, 1977.Google Scholar
  38. [SW]
    Schoening, U. and K.W. Wagner. “Collapsing Oracle Hierarchies, Census Functions, and Logarithmically Many Queries”, STACS '88 Springer-Verlag Lecture Notes in Computer Science, 294:91–97, 1988.Google Scholar
  39. [Sz]
    Szelepcsenyi, R. “The Method of Forcing for Nondeterministic Automata”, The Bulletin on the EATCS, 33:96–100, October 1987.Google Scholar
  40. [To]
    Toda, S. “Σ2 SPACE(n) is Closed Under Complement”, submitted for publication, 1987.Google Scholar
  41. [Wi]
    Wilson, C. “Relativized Circuit Complexity”, Journal of Computer and System Sciences, 31(2):169–181, October 1985.Google Scholar
  42. [Wr]
    Wrathall, C. “Complete Sets and the Polynomial-Time Hierarchy”, Theoretical Computer Science, 3:23–33, 1977.Google Scholar
  43. [Ya]
    Yap, C. “Some Consequences of Non-Uniform Conditions on Uniform Classes”, Theoretical Computer Science, 26:287–300, 1983.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • J. Hartmanis
    • 1
  1. 1.Department of Computer ScienceCornell UniversityIthaca

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