  We study the computational power of machines that specify their own
acceptance types, and show that they accept exactly the languages that
$\manyonesharp$-reduce to NP sets. A natural variant accepts exactly the
languages that $\manyonesharp$-reduce to P sets. We show that these two classes
coincide if and only if $\psone = \psnnoplusbigohone$, where the latter class
denotes the sets acceptable via at most one question to $\sharpp$ followed by
at most a constant number of questions to $\np$.
