Duplication versus Redundancy

N. Lygeros

Translated from the Greek by Athena Kehagias

The notion of repetition (Duplication) and the notion of pleonasm (Redundancy) often cause a conceptual confusion. This derives partly at least, from the relative correlation that exists between the two concepts. This does not mean that there is no difference. There are differences and is quite substantial in many fields, such as genetics, economics, or mathematics, especially in axiomatic maths.
More generally at the gnostic level and more technically at complex networks, the issue of the difference between repetition and redundancy is crucial because the notion of resistance to external attacks is also involved. More specifically, redundancy derives from the existence of a structural correlation which provides the direct access to information, to one of the two ensembles.
While repetition can only be local.
This difference between local and global, explains the conceptual difference of recurrence and redundancy. Furthermore, as the recurrence is local, but can be polytopic, without necessarily been whole. Therefore, the repetition can be used at network as well. While redundancy, even though completely useless at the web systems, is proven to be of the most powerful tools in a critical field. The lack of repetition can be structurally catastrophic, while the same is not applicable to redundancy. Repetition is resistant to external attacks, or to an error of calculation, merely if it belongs to a redundancy system. We can examine this through the normal forms as well.
A table is in normal form, when all of its feature values are simple. With the terminology of the graphics theory, we always have a simple chart rather than a multiple one.
The relationships at their initial normal form, may contain not only repetitions, but also redundancies. And in this case, it would be important that we identify the primary feature which is the key of the relationship or a particle of a key of the relationship.
While, the second normal form, is a first normal form where all non-primary features are fully dependent functionally, to each key of the table. The first normal form tables, are converted into second normal form tables, by the process of disaffiliation. While the third normal form, should not contain functional dependencies between its non-primary features, the second normal form does not contain any redundancies.
Therefore, we can sense, that not only the notions of repetition and redundancy are not the same, but additionally, that their difference is functional and creative through the context of normalization. Normalization does always have a great initial imputed cost. But, this cost will allow in retrospect, efficient calculations where there will be no isomorphisms and groups of automorphisms. Each entity is specific after a normalization, because it is a critical system.

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