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, RSN1-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 RSN1-tt (NP) has many equivalent forms having to do with ordered and parallel access to NP and NP ∩ coNP.
Cite
CITATION STYLE
Hemaspaandra, E., Hemaspaandra, L. A., & Hempel, H. (1997). RSN1-tt (NP) distinguishes robust many-one and Turing completeness. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1203, pp. 49–60). Springer Verlag. https://doi.org/10.1007/3-540-62592-5_60
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