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For example, A system can accept a description of a symbol as "black-heart" or "heart-black". As far as this system is concerned, both description are valid.

Is there a computer science terminology or math concept for the existence of multiple, equivalent codes/representations of a concept/object?

Anthony Kong
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  • I’m not aware of a name for this phenomenon, but for me it’s a sign to dig deeper. Do the two terms really describe the same concept? Are they used in different contexts? By different users? Why are there even two terms? – Rik D Dec 18 '22 at 14:09
  • Your example is about equivalent descriptions, which is a topic of (natural) languages, not computer science or math. But then you ask about equivalent "codes" or "representations", which is pretty vague (and no explaining example). Hence, in the current form, I think the question will encourage too much guessing around and opinionated answers. – Doc Brown Dec 18 '22 at 14:44
  • ... and as if people want to prove my point, we already got two answers including three different guesses. – Doc Brown Dec 19 '22 at 19:30

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One could say that one of the valid values is an alias of the other one.

It's a good idea to have a consistent canonical value and recommend the use of that one, though (for instance, color first always, or shape first always).

Pedro von Hertwig Batista
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You have non-unique representations, or multiple equivalent representations. That’s exactly the terms that are used. There is no single word.

Usually you have one (sometimes several, for example for Unicode graphemes) canonical references to make comparisons easier. The idea is that if you convert all your data to a canonical representation, then checking for equality becomes trivial.

But look at something more complex. “Figures on a chessboard” could be represented as a list of type, colour, position. If there are 32 pieces then you have 32! different representations for the same pieces. You can have a canonical representation: Same list format, but the piece on a1 comes first, then b1, c1 etc. Only one representation. It white figures first, then black, each in the order king, queen etc. You have a different canonical representation. If two boards use the same canonical representation then comparing them is trivial.

Or you could pick one of gazillions of totally different representations.

gnasher729
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Contrary to some comments, I think there is a very straightforward answer here.

A term for different styles of representation of the same information is an encoding.

I don't think there is a specific term for the existence of multiple encodings, since it is such a common thing.

Indeed, "codified" could be a term where multiple representations have been squeezed out, and "codification" for the act of doing so.

Perhaps "uncodified" could be a term when styles of representation are multiple and insufficiently systematic, although it could also have the connotation of there being a single but unsystematic representation (rather than there being multiple styles of representation).

Steve
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  • I doubt "encoding" fits well to the OP's example "black-heart" or "heart-black" - but as I wrote in my comment under the question, this is probably because the example does not fit to the question (for which the OP gave no example). – Doc Brown Dec 19 '22 at 06:03
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The mathematical name for a set of equivalent objects is an equivalence class. Any two objects in the same equivalence class within an equivalence relation are equivalent by that relation.

The Unicode standard defines equivalence classes of names and code points of symbols under various normalization forms.

Clement Cherlin
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