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)


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).


Turing Machine Complexity Class Symmetric Difference Selector Function Polynomial Time Hierarchy 
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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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