Gap theorem

The gap theorem of Borodin is a 1972 report published by Allan Borodin set of complexity theory in theoretical computer science.

The sentence was in 1964 proved by Boris Trakhtenbrot, but in the West remained unheeded.

He says that there are arbitrarily large gaps in the hierarchy of complexity classes.

Formal: For total, computable functions, there are always considered a total and computable function such that:

The above function can not be zeitkonstruierbar, otherwise this would be a contradiction to the hierarchy records, which state that an increase of time or space for a calculation results in an increase in the complexity class.

Example

There are computable functions s, in which:

By application of the void set.