A major open question in communication complexity is if randomized and quantum communication are polynomially related for all total functions. So far, no gap larger than a power o...
—In 1982, Kannan showed that ΣP 2 does not have nk -sized circuits for any k. Do smaller classes also admit such circuit lower bounds? Despite several improvements of Kannan’s...
We prove two main results on how arbitrary linear threshold functions f(x) = sign(w · x − θ) over the n-dimensional Boolean hypercube can be approximated by simple threshold f...
—A simple averaging argument shows that given a randomized algorithm A and a function f such that for every input x, Pr[A(x) = f(x)] ≥ 1−ρ (where the probability is over the...
In [3], the authors introduced the Generalised Character Compatibility Problem as a generalisation of the Perfect Phylogeny Problem for a set of species. This generalised problem t...