Kolmogorov’s very first paper on algorithmic information theory (Kolmogorov, Problemy peredachi infotmatsii 1(1) (1965), 3) was entitled “Three approaches to the definition ...
Andrei E. Romashchenko, Alexander Shen, Nikolai K....
For any q > 1, let MODq be a quantum gate that determines if the number of 1’s in the input is divisible by q. We show that for any q, t > 1, MODq is equivalent to MODt (u...
This paper develops new relationships between resource-bounded dimension, entropy rates, and compression. New tools for calculating dimensions are given and used to improve previo...