## Relative to a random oracle, NP is not small (1994)

Venue: | In Proc. 9th Structures |

Citations: | 18 - 1 self |

### BibTeX

@INPROCEEDINGS{Kautz94relativeto,

author = {Steven M. Kautz and Peter Bro Miltersen},

title = {Relative to a random oracle, NP is not small},

booktitle = {In Proc. 9th Structures},

year = {1994},

pages = {162--174}

}

### OpenURL

### Abstract

Resource-bounded measure as originated by Lutz is an extension of classical measure theory which provides a probabilistic means of describing the relative sizes of complexity classes. Lutz has proposed the hypothesis that NP does not have p-measure zero, meaning loosely that NP contains a non-negligible subset of exponential time. This hypothesis implies a strong separation of P from NP and is supported by a growing body of plausible consequences which are not known to follow from the weaker assertion P ̸ = NP. It is shown in this paper that relative to a random oracle, NP does not have p-measure zero. The proof exploits the following independence property of algorithmically random sequences: if A is an algorithmically random sequence and a subsequence A0 is chosen by means of a bounded Kolmogorov-Loveland