P-Printable Sets

Abstract

P-printable sets arise naturally in the.studies of generalized Kolmogorov complexity and data compression, as well as in other areas. We present new characterizations of the P-printable sets and present necessary and sufficient conditions for the existence of sparse sets in P that are not P-printable. As a corollary to one of our results, we show that the class of sets of small generalized Kolmogorov complexity is exactly the class of sets which are P-isomorphic to a tally language.