Separations by Random Oracles and "Almost" Classes for Generalized Reducibilities

Let ≤r and ≤s be two binary relations on 2N which are meant as reducibilities. Let both relations be closed under finite variation (of their set arguments) and consider the uniform distribution on 2N , which is obtained by choosing elements of 2N by independent tosses of a fair coin. Then we might ask for the probability that the lower ≤r-cone of a randomly chosen set X, that is, the class of all sets A with A ≤r X, differs from the lower ≤s-cone of X. By closure under finite variation, the Kolmogorov 0-1 law yields immediately that this probability is either 0 or 1; in case it is 1, the relations are said to be separable by random oracles. Again by closure under finite variation, for every given set A, the probability that a randomly chosen set X is in the upper ≤r-cone of A is either 0 or 1; let Almostr

• Type: Conference
• Year: 1995
• Where: MFCS
• Authors: Wolfgang Merkle, Yongge Wang
• Keywords: Binary Relations, MFCS 1995, Set Arguments, Theoretical Computer Science, finite Variation