Fixed Parameter Inductive Inference

We investigate a particular inductive inference problem where we are given as input a finite set of ordered triples of the form (wi, bi, ti) such that wi is a bit string, bi is a single bit, and ti is a positive integer written in unary. A machine M is said to match such a triple if M outputs bi on input wi in at most ti steps. We proceed to investigate the fixed parameter problems where we fix the number of triples. We show that the problem for k triples is in P. However, no deterministic machine is known to solve it in less than O(nk) time. These problems are of particular interest in computational complexity theory because allowing O(log(n)) non-deterministic guesses offers a significant improvement from the best known deterministic algorithm.