It is shown that from two strings that are partially random and independent (in the sense of Kolmogorov complexity) it is possible to effectively construct polynomially many strin...
As Bin Packing is NP-hard already for k = 2 bins, it is unlikely to be solvable in polynomial time even if the number of bins is a fixed constant. However, if the sizes of the item...
By the fundamental theorem of symmetric polynomials, if P Q[X1, . . . , Xn] is symmetric, then it can be written P = Q(1, . . . , n), where 1, . . . , n are the elementary symmet...
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 ...