We study the structure of the set of semidualizing complexes over a
local
ring.
In particular, we prove that for a pair of semidualizing complexes
$X_1$
and
$X_2$ such that $G_{X_{2}}\dim X_{1}<\infty $ we have $X_2\simeq
X_1\otimes^{L}_R\func{\mathbf{R}Hom}_R(X_{1},X_{2})$. Specializing to the
case
of
semidualizing modules over artinian rings we obtain a number of
quantitative
results for rings possessing a configuration of semidualizing
modules
of
special form. For rings with ${\mathfrak m}^3=0$ this condition
reduces
to
the existence of a nontrivial semidualizing module and we prove a number of
structural results in this case.