We show the following results regarding complete sets:

NP-complete sets and PSPACE-complete sets are many-one
autoreducible.

Complete sets of any level of PH, MODPH, or
the Boolean hierarchy over NP are many-one autoreducible.

EXP-complete sets are many-one mitotic.

NEXP-complete sets are weakly many-one mitotic.

PSPACE-complete sets are weakly Turing-mitotic.

We investigate the complexity of enumerative approximation of
two elementary problems in linear algebra, computing the rank
and the determinant of a matrix. In particular, we show that
if there exists an enumerator that, given a matrix, outputs a
list of constantly many numbers, one of which is guaranteed to
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Valiant (SIAM Journal on Computing 8, pages 410--421) showed that the
roblem of counting the number of s-t paths in graphs (both in the case
of directed graphs and in the case of undirected graphs) is complete
for #P under polynomial-time one-Turing reductions (namely, some
post-computation is needed to ... more >>>

Is there an NP function that, when given a satisfiable formula
as input, outputs one satisfying assignment uniquely? That is, can a
nondeterministic function cull just one satisfying assignment from a
possibly exponentially large collection of assignments? We show that if
there is such a nondeterministic function, then the polynomial ... more >>>

We characterize the complexity of some natural and important
problems in linear algebra. In particular, we identify natural
complexity classes for which the problems of (a) determining if a
system of linear equations is feasible and (b) computing the rank of
an integer matrix, ... more >>>

In 1978, Hartmanis conjectured that there exist no sparse complete sets
for P under logspace many-one reductions. In this paper, in support of
the conjecture, it is shown that if P has sparse hard sets under logspace
many-one reductions, then P is included in DPSPACE[log^2 n].

It is shown that the PL hierarchy defined in terms of the
standard Ruzzo-Simon-Tompa relativization collapses to PL.