We extend the lower bounds on the complexity of computing Betti numbers proved in [6] to complex algebraic varieties. More precisely, we first prove that the problem of deciding ...
We propose a novel subdivision of the plane that consists of both convex polygons and pseudotriangles. This pseudo-convex decomposition is significantly sparser than either conve...
Oswin Aichholzer, Clemens Huemer, S. Kappes, Betti...
We analyse and compare the complexity of several algorithms for computing modular polynomials. We show that an algorithm relying on floating point evaluation of modular functions...
In a previous paper we have suggested a number of ideas to attack circuit size complexity with cohomology. As a simple example, we take circuits that can only compute the AND of t...
It is known that the classical and quantum query complexities of a total Boolean function f are polynomially related to the degree of its representing polynomial, but the optimal ...