2,393 research outputs found
Kolmogorov Random Graphs and the Incompressibility Method
We investigate topological, combinatorial, statistical, and enumeration
properties of finite graphs with high Kolmogorov complexity (almost all graphs)
using the novel incompressibility method. Example results are: (i) the mean and
variance of the number of (possibly overlapping) ordered labeled subgraphs of a
labeled graph as a function of its randomness deficiency (how far it falls
short of the maximum possible Kolmogorov complexity) and (ii) a new elementary
proof for the number of unlabeled graphs.Comment: LaTeX 9 page
Boltzmann samplers for random generation of lambda terms
Randomly generating structured objects is important in testing and optimizing
functional programs, whereas generating random -terms is more specifically
needed for testing and optimizing compilers. For that a tool called QuickCheck
has been proposed, but in this tool the control of the random generation is
left to the programmer. Ten years ago, a method called Boltzmann samplers has
been proposed to generate combinatorial structures. In this paper, we show how
Boltzmann samplers can be developed to generate lambda-terms, but also other
data structures like trees. These samplers rely on a critical value which
parameters the main random selector and which is exhibited here with
explanations on how it is computed. Haskell programs are proposed to show how
samplers are actually implemented
- …