Although tally sets are generally considered to be weak when used as oracles, it is shown here that in relativizing certain complexity classes, they are in fact no less powerful than any other class of sets and are more powerful than the class of recursive sets. More specifically, relativizations of the classes of P-printable sets and sets with small Generalized Kolmogorov complexity (SGK) are studied. It is shown here that all sparse sets are PTALLY -printable and are in SGKTALLY , and that there are self-P-printable sets that are neither PREC-printable nor in SGKREC . There are also sets that are PREC-printable and in SGKREC that are not self-P-printable. Relativizations to various subrecursive oracles are also presented. A restriction on the number of oracle queries is also presented, with the result that relativizing SGK to any oracle with at most O(log n) queries results in a set that is still in SGK.
Rubinstein, Roy S.
(1992). Relativizations of the P-Printable Sets and the Sets with Small Generalized Kolmogorov Complexity. .
Retrieved from: https://digitalcommons.wpi.edu/computerscience-pubs/185