Comparison between the complexity of afunction and the complexity of its graphBruno

This paper investigates in terms of Kolmogorov complexity the diierences between the information necessary to compute a recursive function and the information contained in its graph. Our rst 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. RRsumm Nous tudions en termes de complexitt de Kolmogorov les diiirences entre l'in-formation nncessaire au calcul d'une fonction rrcursive et l'information conte-nue dans son graphe. Nous montrons que la complexitt des segments initiaux de ce graphe, bien que bornne n'a presque jamais de limite. Notre second rrsul-tat est que la complexitt de ces segments initiaux approche celle de la fonction dans la plupart des cas (et en moyenne), mais pas toujours. Abstract This paper investigates in terms of Kolmogorov complexity the diier-ences between the information necessary to compute a recursive function and the information contained in its graph. Our rst 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.