Prediction of the next value of a function

Abstract

The following model of inductive inference is considered. Arbitrary set tau = {tau_1, tau_2, ..., tau_n} of n total functions N->N is fixed. A "black box" outputs the values f(0), f(1), ..., f(m), ... of some function f from the set tau. Processing these values by some algorithm (a strategy) we try to predict f(m+1) from f(0), f(1), ..., f(m). Upper and lower bounds for average error numbers are obtained for prediction by using deterministic and probabilistic strategies.