Abstract

Introduction One can make a strong case for that an unsurpassed model of any set of observations, generated by some physical machinery, is provided by the shortest program for a universal computer with which the data can be reproduced. Indeed, such a program must take advantage of all the constraints that the data have, and hence it will capture the relevant properties of the machinery - provided of course that the data set is large enough to reflect them. Unfortunately, such a program or even its length, the celebrated Kolmogorov complexity, cannot be found by algorithmic means, which has the devastating implication that, even though we can estimate it from above, we cannot assess the goodness of the estimate. And this puts an end to the dreams of basing inductive inference on the Kolmogorov complexity. The problem of noncomputability can be overcome, while retaining the idea of measuring the strength of constraints by code length, if we select a smaller class of `codes' as `

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