Big omega versus the wild functions

@article{Vitnyi1985BigOV,
  title={Big omega versus the wild functions},
  author={Paul M. B. Vit{\'a}nyi and Lambert Meertens},
  journal={SIGACT News},
  year={1985},
  volume={16},
  pages={56-59}
}
The question of the desirable properties and proper definitions of the Order-of-Magnitude symbols, in particular O and Ø, is addressed once more. The definitions proposed are chosen for complementary mathematical properties, rather than for similarity of form. 

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In a well-known SIGACT/NEWS paper, Knuth sets forth the asymptotic notation by which the authors all now live and proposes that members of SIGACT adopt the O, Ω and Θ notations unless a better alternative can be found reasonably soon.

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It is proved that the primitive properties are equivalent to the definition of the O-notation as linear dominance, and it is defined as a general tool for manipulating theO-notation, and shown that Master theorems hold under linear dominance.

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    International Journal of Modern Nonlinear Theory and Application
  • 2022
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The concept of Dimensional complexity in algorithmic e ciency is introduced and it is deduced that an optimally e cient algorithm has zero Time complexity, zero Space complexity, and an in nite D dimensional complexity.

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The methods are used to characterize in terms of oracle Turing machines the classes defined by exponential lower bounds on some nonuniform complexity measures, obtaining an unified approach to deal with upper and lower bounds.

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Two decades of applied Kolmogorov complexity: in memoriam Andrei Nikolaevich Kolmogorov 1903-87

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    [1988] Proceedings. Structure in Complexity Theory Third Annual Conference
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The authors provide an introduction to the main ideas of Kolmogorov complexity and survey the wealth of useful applications of this notion. It is based on a theory of information content of strings,

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