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We consider the following question: Can every efficiently samplable distribution be efficiently sampled, up to a small statistical distance, using roughly as much randomness as the length of its output? Towards a study of this question we generalize the current theory of pseudorandomness and consider pseudorandom generators that fool non-boolean distinguishers (nb-PRGs). We show a link between nb-PRGs and a notion of function compression, introduced by Harnik and Naor 16. (A compression algorithm for f should efficiently compress an input x in a way that will preserve the information needed to compute f(x).) By constructing nb-PRGs, we answer the above question affirmatively under the following types of assumptions:
Dubrov et al. (Sun,) studied this question.