 
Summary: SEPARATION OF NPCOMPLETENESS NOTIONS
A. PAVAN
AND ALAN L SELMAN
Abstract. We use hypotheses of structural complexity theory to separate various NPcompleteness notions. In particular, we
introduce an hypothesis from which we describe a set in NP that is
¡
P
Tcomplete but not
¡
P
ttcomplete. We provide fairly thorough
analyses of the hypotheses that we introduce.
Key words. Turing completeness, truthtable completeness, manyone completeness, pselectivity, pgenericity
AMS subject classifications.
1. Introduction. Ladner, Lynch, and Selman [LLS75] were the first to compare the strength of polyno
mialtime reducibilities. They showed, for the common polynomialtime reducibilities, Turing (¢
P
T), truth
table (¢
