Randomness behaviour in blum universal static complexity spaces

Abstract

In this paper we prove that plain complexity induces the weakest form of randomness for all Blum Universal Static Complexity Spaces [11]. As a consequence, there is all infinite sequences have an infinite number of non-random prefixes with respect to any given Blum Universal Static Complexity Space. This is a generalization of the result obtained by Solovay [27] and Calude [7] for plain complexity, and also of the result obtained by Câmpeanu [10], and independently, later on, by Bienvenu and Downey in [1] for prefix-free complexity. © 2012 Springer-Verlag Berlin Heidelberg.