In this paper, we propose a quantification of distributions on a setof strings, in terms of how close to pseudorandom the distributionis. The quantification is an adaptation of the theory of dimension ofsets of infinite sequences first introduced by Lutzcite{Lutz:DISS}. We show that this definition is robust, by considering an alternate, equivalentquantification. It is known that pseudorandomness can be characterizedin terms of predictors cite{Yao82a}. Adapting Hitchcockcite{Hitchcock:FDLLU}, we show that the log-loss function incurred bya predictor on a distribution is quantitatively equivalent to thenotion of dimension we define. We show that every distribution on aset of strings of length n has a dimension s[01] , and forevery s[01] there is a distribution with dimension s. Westudy some natural properties of our notion of dimension.Further, we propose an application of our quantification to thefollowing problem. If we know that the dimension of a distribution onthe set of n-length strings is s[01] , can wedeterministically extract out sn emph{pseudorandom} bits out of thedistribution? We show that this is possible in a special case - anotion analogous to the bit-fixing sources introduced by Choremph{et. al.} cite{CGHFRS85}, which we term a emph{nonpseudorandombit-fixing source}. We adapt the techniques of Kamp and Zuckermancite{KZ03} and Gabizon, Raz and Shaltiel cite{GRS05} to establishthat in the case of a non-pseudorandom bit-fixing source, we candeterministically extract the pseudorandom part of thesource. Further, we show that the existence of optimal nonpseudorandomgenerator is enough to show P=BPP.
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