Inductive inference of recursive functions: complexity bounds
Zusammenfassung
This survey includes principal results on complexity
of inductive inference for recursively enumerable classes of total
recursive functions. Inductive inference is a process to find an
algorithm from sample computations. In the case when the given class
of functions is recursively enumerable it is easy to define a
natural complexity measure for the inductive inference, namely, the
worst-case mindchange number for the first n functions in the given
class. Surely, the complexity depends not only on the class, but
also on the numbering, i.e. which function is the first, which one
is the second, etc. It turns out that, if the result of inference is
Goedel number, then complexity of inference may vary between
log n+o(log2n ) and an arbitrarily slow recursive function. If the
result of the inference is an index in the numbering of the
recursively enumerable class, then the complexity may go up to
const-n. Additionally, effects previously found in the Kolmogorov
complexity theory are discovered in the complexity of inductive
inference as well.