... The information contained in a string x about a string y is the difference between the Kolmogorov complexity of y and the conditional Kolmogorov complexity of y given x, i.e., I (x : y ) = C(y ) - C(y | ... On the other hand, for nondeterministic polynomial time distinguishing complexity with randomness, CAMDpoly , we show that symmetry of information holds for most pairs of strings in any set in NP. ... Is there an assumption weaker than P=NP which implies polynomial time symmetry of information? ...