skip to main content
article
Free Access

A moment of perfect clarity II: consequences of sparse sets hard for NP with respect to weak reductions

Published:01 December 2000Publication History
Skip Abstract Section

Abstract

This issue's column, Part II of the article started in the preceding issue, is about progress on the question of whether NP has sparse hard sets with respect to weak reductions.Upcoming Complexity Theory Column articles include A. Werschulz on information-based complexity; J. Castro, R. Gavaldà, and D. Guijarro on what complexity theorists can learn from learning theory; S. Ravi Kumar and D. Sivakumar on a to-be-announced topic; M. Holzer and P. McKenzie on alternating stack machines; and R. Paturi on the complexity of k-SAT.

References

  1. {AHH+93} V. Arvind, Y. Han, L. Hemachandra, J. Köbler, A. Lozano, M. Mundhenk, M. Ogiwara, U. Schöning, R. Silvestri, and T. Thierauf. Reductions to sets of low information content. In K. Ambos-Spies, S. Homer, and U. Schöning, editors, Complexity Theory, pages 1-45. Cambridge University Press, 1993. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. {AKM96} V. Arvind, J. Köbler, and M. Mundhenk. Upper bounds for the complexity of sparse and tally descriptions. Mathematical Systems Theory, 29:63-94, 1996.Google ScholarGoogle ScholarCross RefCross Ref
  3. {BFT97} H. Buhrman, L. Fortnow, aud L. Torenvliet. Six hypotheses in search of a theorem. In Proceedings of the 12th Annual IEEE Conference on Computational Complexity, pages 2-12. IEEE Comptuer Society Press, 1997. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. {CHW99} J. Cai, L. Hemaspaandra, and G. Wechsung. Robust reductions. Theory of Computing Systems, 32(6):625-647, 1999.Google ScholarGoogle ScholarCross RefCross Ref
  5. {CNS95} J. Cai, A. Naik, and D. Sivakumar. On the existence of hard sparse sets under weak reductions. Technical Report 95-31, Department of Computer Science, State University of New York at Buffalo, Buffalo, NY, July 1995.Google ScholarGoogle Scholar
  6. {CO97} J. Cai and M. Ogihara. Sparse sets versus complexity classes. In L. Hemaspaandra and A. Selman, editors, Complexity Theory Retrospective II, pages 53-80. Springer-Verlag, 1997. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. {GH00} C. Glaßer and L. Hemaspaandra. A moment of perfect clarity I: The parallel census technique. SIGACT News, 31(3):37-42, 2000. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. {Gla00} C. Glaßer. Consequences of the existence of sparse sets hard for NP under a subclass of truth-table reductions. Technical Report TR 245, Institut für Informatik, Universität Würzburg, Würzburg, Germany, January 2000.Google ScholarGoogle Scholar
  9. {HOW92} L. Hemachandra, M. Ogiwara, and O. Watanabe. How hard are sparse sets? In Proceedings of the 7th Structure in Complexity Theory Conference, pages 222-238. IEEE Computer Society Press, June 1992.Google ScholarGoogle ScholarCross RefCross Ref
  10. {Kad89} J. Kadin. pNP{log n} and sparse Turing-complete sets for NP. Journal of Computer and System Sciences, 39(3):282-298, 1989.Google ScholarGoogle ScholarCross RefCross Ref
  11. {KW99} J. Köbler and O. Watanabe. New collapse consequences of NP having small circuits. SIAM Journal on Computing, 28(1):311-324, 1999. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. {LLS75} R. Ladner, N. Lynch, and A. Selman. A comparison of polynomial time reducibilities. Theoretical Computer Science, 1(2):103-124, 1975.Google ScholarGoogle ScholarCross RefCross Ref
  13. {Mah82} S. Mahaney. 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 ScholarGoogle ScholarCross RefCross Ref
  14. {Mah86} S. Mahaney. Sparse sets and reducibilities. In R. Book, editor, Studies in Complexity Theory, pages 63-118. John Wiley and Sons, 1986.Google ScholarGoogle Scholar
  15. {OW91} M. Ogiwara and O. Watanabe. On polynomial-time bounded truth-table reducibility of NP sets to sparse sets. SIAM Journal on Computing, 20(3):471-483, June 1991. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. {Siv00} D. Sivakumar, May 6, 2000. Personal Communication.Google ScholarGoogle Scholar
  17. {vM97} D. van Melkebeek, 1997. Personal Communication.Google ScholarGoogle Scholar
  18. {VV86} L. Valiant and V. Vazirani. NP is as easy as detecting unique solutions. Theoretical Computer Science, 47:85-93, 1986. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. {You92} P. Young. How reductions to sparse sets collapse the polynomial-time hierarchy: A primer. SIGACT News, 1992. Part I (#3, pages 107-117), Part II (#4, pages 83-94), and Corrigendum to Part I (#4, page 94). Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. A moment of perfect clarity II: consequences of sparse sets hard for NP with respect to weak reductions

        Recommendations

        Comments

        Login options

        Check if you have access through your login credentials or your institution to get full access on this article.

        Sign in

        Full Access

        • Published in

          cover image ACM SIGACT News
          ACM SIGACT News  Volume 31, Issue 4
          Dec. 2000
          78 pages
          ISSN:0163-5700
          DOI:10.1145/369836
          Issue’s Table of Contents

          Copyright © 2000 Authors

          Publisher

          Association for Computing Machinery

          New York, NY, United States

          Publication History

          • Published: 1 December 2000

          Check for updates

          Qualifiers

          • article

        PDF Format

        View or Download as a PDF file.

        PDF

        eReader

        View online with eReader.

        eReader