INDUCTIVE INFERENCE OF LIMITING PROGRAMS WITH BOUNDED NUMBER OF MIND CHANGES

Abstract

We consider inductive inference of total recursive functions in the case, when produced hypotheses are allowed some finite number of times to change “their mind” about each value of identifiable function. Such type of identification, which we call inductive inference of limiting programs with bounded number of mind changes, by its power lies somewhere between the traditional criteria of inductive inference and recently introduced inference of limiting programs. We consider such model of inductive inference for EX and BC types of identification, and we study • tradeoffs between the number of allowed mind changes and the number of anomalies, and • relations between classes of functions identifiable with different probabilities. For the case of probabilistic identification we establish probabilistic hierarchies which are quite unusual for EX and BC types of inference.