#sequences, combinations and uniqueness.

8 messages · Page 1 of 1 (latest)

zenith ridge
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Does there exist such a property, such that you can take any two or more different fixed length sequences, and combine them into a third unique sequence, with a guarantee of having no collisions from other sequences made by different set of start sequences?

ie, just as an example for something that doesn't have this property, a bitpattern and something like a bitmask and bitwise operations.
s{1} = 101101011101001
s{2} = 101101011101001
s{n} = ...
S = s{1} \vee s{2} \vee ... s{n}

In this case, there are multiple ways to get the same resulting bitpattern S, which is what we want to avoid.

So the question is, if there exists such a property/function, so that for every unique set of different {s{1}, s{2}, ..., s{n}} sequences, there is only one unique result sequence S? ie S = f({s{1},s{2}) = f({s{2},s_{1}), such that there exists no different result sequence S2 which contains exactly s{1} and s{2} and that there exists no other S{other}=S which which contains something different than the set {s{1},s{2}} but results in the same S. So in a hash function the order of operations would matter, so I don't think that's applicable here?

lime wyvernBOT
vivid skiff
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does that have to hold?

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or they can be three different lengths?

zenith ridge
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Whatever assumption makes the other attributes hold, so if they can be different lengths, especially the output length, it makes it possible to encode more information in the output string without imposing requirements of fixed length widths. But at the same time, I think one would loose information about the fixed length input, but that assumption might not be helpful anyway 🤔

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I think that imposing a limit to the output length might impose limits on the input lengths, so that if you would want a certain output length that would put restrictions on the input. Otherwise a fixed output length could be set, but a bit like a hash function, the problem is that it is order dependent, and a one way function, so I don't think it can satisfy the requirements.

zenith ridge
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I just realized this whole thing probably falls under lossless compression algorithms, which I'm going to explore now