# Comparison between the complexity of a function and the complexity of its graph

Contributed Papers Picture Languages - Function Systems/Complexity

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## Abstract

This paper investigates in terms of *Kolmogorov complexity* the differences between the information necessary to compute a recursive function and the information contained in its graph. Our first result is that the complexity of the initial parts of the graph of a recursive function, although bounded, has almost never a limit. The second result is that the complexity of these initial parts approximate the complexity of the function itself in most cases (and in the average) but not always.

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© Springer-Verlag Berlin Heidelberg 1998