Theory of Computing Systems

, Volume 63, Issue 3, pp 386–393 | Cite as

Nondeterminisic Sublinear Time Has Measure 0 in P

  • John M. HitchcockEmail author
  • Adewale Sekoni


The measure hypothesis is a quantitative strengthening of the \(\mathrm {P} \neq \text {NP}\) conjecture which asserts that \(\text {NP}\) is a nonnegligible subset of \(\text {EXP}\). Cai et al. (1997) showed that the analogue of this hypothesis in \(\mathrm {P}\) is false. In particular, they showed that \(\text {NTIME}[n^{1/11}]\) has measure 0 in \(\mathrm {P}\). We improve on their result to show that the class of all languages decidable in nondeterministic sublinear time has measure 0 in \(\mathrm {P}\). Our result is based on DNF width and holds for all four major notions of measure on \(\mathrm {P}\).


Nondeterministic time DNF width Resource-bounded measure 



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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of WyomingLaramieUSA

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