In this note, we use lower bounds on Boolean multiplicative complexity to prove lower bounds on Boolean circuit complexity. We give a very simple proof of a 7n/3 − c lower bound ...
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 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...
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 ...
Abstract. Given a simplicial hyperplane arrangement H and a subspace arrangement A embedded in H, we define a simplicial complex ∆A,H as the subdivision of the link of A induced...