Inductive inference and unsolvability

Abstract

AbtractIt is shown that many different problems have the same degree of unsolvability. Among these problems are:The Inductive Inference Problem. Infer in the limit an index for a recursive function f presented as f(0), f(1),f(2),….The Recursive Index Problem. Decide in the limit if i is the index of a total recursive function.The Zero Nonvariant Problem. Decide in the limit if a recursive function f presented as f(0), f(1), f(2),… has value unequal to zero for infinitely many arguments.Finally, it is shown that these unsolvable problems are strictly easier than the halting problem.