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On symmetric differences of NP-hard sets with weakly-P-selective sets

  • Bin Fu
  • Hong-zhou Li
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 650)

Abstract

The symmetric differences of N P—hard sets with weakly — P-selective sets are investigated in this paper. We show that if there exist a weakly-P-selective set A and a NP-≤ m p -hard set H such that H-AP btt (Sparse) and A-H ∃ Pm (Sparse) then P=N P So no NP-≤ m p -hard set has sparse symmetric difference with any weakly-P-selective set unless P=N P. In addition we show there exists a P-selective set which has exponentially dense symmetric difference with every set in Pbtt(Sparse).

Keywords

Turing Machine Complexity Class Symmetric Difference Selector Function Polynomial Time Hierarchy 
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Reference

  1. [BGS88]
    J.Balcarzar, J.Diaz, and J.Gabarro: Structural Complexity I,II. Springer-Verlag, 1988 and 1990.Google Scholar
  2. [BK87]
    R.Book and K.Ko: On Sets Truth-table Reducible to Sparse Sets. SIAM J.Computing 17(1988), 903–919.CrossRefGoogle Scholar
  3. [F91]
    B.Fu: On Lower Bounds of the Closeness between Complexity Classes. To appear in Math. Sys.Theory.Google Scholar
  4. [FL92]
    B.Fu and H.Li: On Closeness of NP-Hard sets to other Complexity Classes. Proc.7th Annual Conference in structural complexity theory, IEEE, 1992, 243–248.Google Scholar
  5. [K83]
    K.Ko: On Self-reducibility and Weakly-P-selectivity. J.of Comp. and Sys.Sci. 26(1983), 209–211.CrossRefGoogle Scholar
  6. [K88]
    K.Ko: Distinguishing Bounded Reducibility by Sparse Sets. Proc.3th Conference on Structural Complexity Theory, IEEE, 1988, 181–191.Google Scholar
  7. [Ma82]
    S.Mahaney: Sparse Complete Sets for NP:Solution of a Conjecture of Berman and Hartmanis. J.Comput.Sys.Sci. 25(1982), 130–143.CrossRefGoogle Scholar
  8. [OW90]
    M.Ogiwara and O.Watanabe: On Polynomial-Time Bounded Truth-table Reducibility of NP sets to Sparse Sets. Proc. of the 22th ACM Symposium on Theory of Computing, 1990, 457–467.Google Scholar
  9. [Sc86]
    U.Schöning: Complete Sets and Closeness to Complexity Classes. Math.Sys. Theory, 13(1986), 55–65.Google Scholar
  10. [Se79]
    A.L.Selman: P-selective Sets, Tally Languages and the Behavior of Polynomial-Time Reducibility on NP. Math.Sys.Theory 13(1981), 326–332.Google Scholar
  11. [Se81]
    A.L.Selman: Some Observation on NP Real Numbers and P-Selective Sets. J. Comput. Sys. Sci. 19(1981), 326–332.CrossRefGoogle Scholar
  12. [Se82]
    A.L.Selman:Reductions on NP and P-selective Sets. Theoret.Comput.Sci. 19 (1982), 287–304.CrossRefGoogle Scholar
  13. [TFL91]
    S.Tang, B.Fu and T.Liu: Exponential Time and Subexponential Time Sets. Proc.6th Annual Conference in structural complexity theory, IEEE, 1991, 230–237.Google Scholar
  14. [T91]
    S.Toda: On Polynomial-Time Truth Table Reducibility of Intractable Sets to P-Selective Sets. Math.Sys.Theory 24(1991), 69–82.Google Scholar
  15. [Y83]
    Y.Yesha: On Certain Polynomial-Time Truth-table Reducibilities of Complete Sets to Sparse Sets. SIAM J.Comput. 12(1983), 411–425.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Bin Fu
    • 1
    • 2
  • Hong-zhou Li
    • 3
  1. 1.Department of Computer ScienceBeijing Computer InstituteBeijingP.R.China
  2. 2.Beijing Laboratory of Cognitive ScienceThe University of Science and Technology of ChinaChina
  3. 3.Department of MathematicsYunnan Education CollegeKunmingP.R.China

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