The strongly bounded Turing reducibilities r = cl (computable Lipschitz reducibility) and r = ibT (identity bounded Turing reducibility) are defined in terms of Turing reductions where the use function is bounded by the identity function up to an additive constant and the identity function, respectively. We show that, for r = ibT, cl, every computably enumerable (c.e.) r-degree a > 0 has the an...

Let f be a computable function from finite sequences of 0’s and 1’s to real numbers. We prove that strong f -randomness implies strong f randomness relative to a PA-degree. We also prove: if X is strongly f -random and Turing reducible to Y where Y is Martin-Löf random relative to Z, then X is strongly f -random relative to Z. In addition, we prove analogous propagation results for other notion...

Recently, the usage of 360-degree videos has prevailed in various sectors such as education, real estate, medical, entertainment and more. The development Virtual World “Metaverse” demanded a Reality (VR) environment with high immersion smooth user experience. However, challenges are faced to provide real-time streaming due nature high-resolution bandwidth requirement, computing power low delay...