Are the outputs of #P functions "random"? We way phrase this question more precisely: are there #P functions whose outputs cannot in general be compressed into a string of small length, and recovered quickly from that string, also given the input as additional information? We prove that the answer to this question is "yes" if and only if P ¿ PP.
CitationGreen, F.; Toran, J. Kolmogorov complexity of #P functions. 1991.