Following the approach of Hemaspaandra and Vollmer, we can define
counting complexity classes #.C for any complexity class C of decision
problems. In particular, the classes #.Pi_{k}P with k >= 1
corresponding to all levels of the polynomial hierarchy have thus been
studied. However, for a large variety of counting ... more >>>

In this work we relate the deterministic
complexity of factoring polynomials (over
finite
fields) to certain combinatorial objects we
call
m-schemes. We extend the known conditional
deterministic subexponential time polynomial
factoring algorithm for finite fields to get an
underlying m-scheme. We demonstrate ... more >>>

An algebraic source is a random variable distributed
uniformly over the set of common zeros of one or more multivariate
polynomials defined over a finite field $F$. Our main result is
the construction of an explicit deterministic extractor for
algebraic sources over exponentially large prime fields. More
precisely, we give ... more >>>