# 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.

## 9 Citations

### A General Definition of the O-notation for Algorithm Analysis

- Computer Science, MathematicsBull. EATCS
- 2015

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.

### Crusade for a better notation

- PhysicsSIGA
- 1985

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.

### O-notation in algorithm analysis

- Computer Science, Mathematics
- 2013

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.

### Dimensional Complexity & Algorithmic Efficiency

- Computer ScienceInternational Journal of Modern Nonlinear Theory and Application
- 2022

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.

### Nonuniform Complexity Classes Specified by Lower and Upper Bounds

- Computer ScienceRAIRO Theor. Informatics Appl.
- 1989

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.

### Dimensional Complexity and Algorithmic Efficiency

- Computer ScienceArXiv
- 2022

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.

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

- Computer Science[1988] Proceedings. Structure in Complexity Theory Third Annual Conference
- 1988

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,…

### Kolmogorov Complexity and its Applications

- Computer ScienceHandbook of Theoretical Computer Science, Volume A: Algorithms and Complexity
- 1990

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