Inductive inference with bounded number of mind changes

Inductive inference machines (IIMs) synthesize programs, given their intended input-output behavior. The program synthesis is viewed as a potentially infinite process of learning by example. Smith [20] studied team learning and obtained results that characterized trade-offs between the number of machines and resources in the learning process. Pitt [16] defined probabilistic learning and showed that ‘probabilistic learning’ is the same as ‘team learning’. Later [17] introduced probabilistic team learning and compared probabilistic team learning and team learning. However, for any given team when we restrict amount of resources allotted for each IIM, then most of the above results fail to hold. This paper studies the relationships between team learning, probabilistic learning and probabilistic team learning when limited resources are available. Some preliminary results obtained indicates a very interesting relationship between them. The proofs for some of the preliminary results, used n-ary recursion theorems, and some complex diagonalization.