We consider the computational complexity of some problems
dealing with matrix rank. Let E,S be subsets of a
commutative ring R. Let x_1, x_2, ..., x_t be variables.
Given a matrix M = M(x_1, x_2, ..., x_t) with entries
chosen from E union {x_1, x_2, ..., ... more >>>

We consider the conjecture stating that a matrix with rank
$o(n)$ and ones on the main diagonal must contain nonzero
entries on a $2\times 2$ submatrix with one entry on the main
diagonal. We show that a slightly stronger conjecture implies
that ... more >>>

Several researchers, including Leonid Levin, Gerard 't Hooft, and
Stephen Wolfram, have argued that quantum mechanics will break down
before the factoring of large numbers becomes possible. If this is
true, then there should be a natural "Sure/Shor separator" -- that is,
a set of quantum ... more >>>