RSN1-tt(NP) Distinguishes Robust Many-One and Turing Completeness

@article{Hemaspaandra1998RSN1ttNPDR,
  title={RSN1-tt(NP) Distinguishes Robust Many-One and Turing Completeness},
  author={E. Hemaspaandra and L. A. Hemaspaandra and H. Hempel},
  journal={Theory of Computing Systems},
  year={1998},
  volume={31},
  pages={307-325}
}
Abstract. Do complexity classes have many-one complete sets if and only if they have Turing-complete sets? We prove that there is a relativized world in which a relatively natural complexity class—namely, a downward closure of NP, $ {{\rm R}_{1\mbox{-}{tt}}^{\cal SN}({\rm NP})} $ —has Turing-complete sets but has no many-one complete sets. In fact, we show that in the same relativized world this class has 2-truth-table complete sets but lacks 1-truth-table complete sets. As part of the… Expand
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