Summary: SEPARATION OF NP-COMPLETENESS NOTIONS
AND ALAN L SELMAN
Abstract. We use hypotheses of structural complexity theory to separate various NP-completeness notions. In particular, we
introduce an hypothesis from which we describe a set in NP that is
T-complete but not
tt-complete. We provide fairly thorough
analyses of the hypotheses that we introduce.
Key words. Turing completeness, truth-table completeness, many-one completeness, p-selectivity, p-genericity
AMS subject classifications.
1. Introduction. Ladner, Lynch, and Selman [LLS75] were the first to compare the strength of polyno-
mial-time reducibilities. They showed, for the common polynomial-time reducibilities, Turing (¢