Nondeterminisic Sublinear Time Has Measure 0 in P
Computational Complexity
2018-01-19 v1
Abstract
The measure hypothesis is a quantitative strengthening of the P != NP conjecture which asserts that NP is a nonnegligible subset of EXP. Cai, Sivakumar, and Strauss (1997) showed that the analogue of this hypothesis in P is false. In particular, they showed that NTIME[n^{1/11}] has measure 0 in P. We improve on their result to show that the class of all languages decidable in nondeterministic sublinear time has measure 0 in P. Our result is based on DNF width and holds for all four major notions of measure on P.
Cite
@article{arxiv.1801.05884,
title = {Nondeterminisic Sublinear Time Has Measure 0 in P},
author = {John M. Hitchcock and Adewale Sekoni},
journal= {arXiv preprint arXiv:1801.05884},
year = {2018}
}