Hardness amplification results show that for every function $f$ there exists a function $Amp(f)$ such that the following holds: if every circuit of size $s$ computes $f$ correctly on at most a $1-\delta$ fraction of inputs, then every circuit of size $s'$ computes $Amp(f)$ correctly on at most a $1/2+\eps$ ... more >>>

We prove the computational hardness of three k-clustering problems using an (almost) arbitrary Bregman divergence as dissimilarity measure: (a) The Bregman k-center problem, where the objective is to find a set of centers that minimizes the maximum dissimilarity of any input point towards its closest center, and (b) the Bregman ... more >>>

In \cite{shenpapier82}, it is shown that four basic functional properties are enough to characterize plain Kolmogorov complexity, hence obtaining an axiomatic characterization of this notion. In this paper, we try to extend this work, both by looking at alternative axiomatic systems for plain complexity and by considering potential axiomatic systems ... more >>>