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RSN 1-tt (NP) Distinguishes Robust Many-One and Turing Completeness

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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 groundwork for our result, we prove that \( {{\rm R}_{1\mbox{-}{tt}}^{\cal SN}({\rm NP})} \) has many equivalent forms having to do with ordered and parallel access to NP and NP ∩ coNP.

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Received November 1996, and in final form July 1997.

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Hemaspaandra, E., Hemaspaandra, L. & Hempel, H. RSN 1-tt (NP) Distinguishes Robust Many-One and Turing Completeness . Theory Comput. Systems 31, 307–325 (1998). https://doi.org/10.1007/s002240000090

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  • DOI: https://doi.org/10.1007/s002240000090

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