1 research outputs found
Towards an axiomatic system for Kolmogorov complexity
In [She82], 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 for other types of complexity. First we
show that the axiomatic system given by Shen cannot be weakened (at least in
any natural way). We then give an analogue of Shen's axiomatic system for
conditional complexity. In a the second part of the paper, we look at
prefix-free complexity and try to construct an axiomatic system for it. We show
however that the natural analogues of Shen's axiomatic systems fails to
characterize prefix-free complexity