Comparing various concepts of function prediction. Part 1.

Abstract

Prediction: f(m+1) is guessed from given f(0), ..., f(m). Program synthesis: a program computing f is guessed from given f(0), ..., f(m). The hypotheses are required to be correct for all sufficiently large m, or with some positive frequency. These approaches yield a hierarchy of function prediction and program synthesis concepts. The comparison problem of the concepts is solved.