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MFCS

1995

Springer

1995

Springer

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

Related Content

Added |
26 Aug 2010 |

Updated |
26 Aug 2010 |

Type |
Conference |

Year |
1995 |

Where |
MFCS |

Authors |
Wolfgang Merkle, Yongge Wang |

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