R1-ttSN(NP) Distinguishes Robust Many-One and Turing Completeness

  title={R1-ttSN(NP) Distinguishes Robust Many-One and Turing Completeness},
  author={Edith Hemaspaandra and Lane A. Hemaspaandra and Harald Hempel},
Do complexity classes have many-one complete sets if and only if they have Turingcomplete sets? We prove that there is a relativized world in which a relatively natural complexity class—namely a downward closure of NP, R 1-tt(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 groundwork for our result, we prove that R 1-tt(NP) has many… CONTINUE READING