Nondeterminisic Sublinear Time Has Measure 0 in P

John M. Hitchcock; Adewale Sekoni

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arXiv · 1801.05884

Nondeterminisic Sublinear Time Has Measure 0 in P

John M. Hitchcock·Adewale Sekoni

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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.

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John M. Hitchcock, Adewale Sekoni. 2018-01-17. Nondeterminisic Sublinear Time Has Measure 0 in P. https://arxiv.org/abs/1801.05884

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