3 years ago

Nondeterminisic Sublinear Time Has Measure 0 in P.

Adewale Sekoni, John M. Hitchcock

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.

Publisher URL: http://arxiv.org/abs/1801.05884

DOI: arXiv:1801.05884v1

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