A generalization of Levin-Schnorr's theorem

Abstract

In this paper, we will generalize the definition of partially random or complex reals, and then show the duality of random and complex, i.e., a generalized version of Levin-Schnorr's theorem. We also study randomness from the view point of arithmetic using the relativization to a complete ${\Pi }_1^0$-class.

11 pages

References in corpus (1)

• A Generalization of Chaitin's Halting Probability Ωand Halting Self-Similar Sets