There are plenty of other reference materials posted in my questions and publications on ResearchGate. I think it is not enough for someone to claim that the sequences I've found are pseudo-random, as their suggestion of a satisfying answer to the question here posed.
If indeed complexity of a sequence is reflected within the algorithm that generates the sequence, then we should not find that high-entropy sequences are easily described by algorithmic means.
I have a very well defined counter example.
Indeed, so strong is the example that the sound challenge is for another researcher to show how one of my maximally disordered sequences can be altered such that the corresponding change to measured entropy is a positive, non-zero value.
Recall that with arbitrarily large hardware registers and an arbitrarily large memory, our algorithm will generate arbitrarily large, maximally disordered digit sequences; no algorithm changes are required. It is a truly simple algorithm that generates sequences that always yield a measure of maximal entropy.
In what way are these results at odds, or in keeping, with Kolmogorov?
If you have a "truly simple" and deterministic algorithm, it is pseudo-random by definition; I presume that simply by using your algorithm, I can also proceed from one state to the next state in lock-step with your sequence. Which makes the entropy measure irrelevant, your sequence is perfectly predictable and therefore not random.
That is what pseudo-random means! It means a sequence is produced by a deterministic process that appears to be random (but is not). It sounds like you have a good pseudo-random algorithm, but unless you are accessing some kind of hardware that is sampling a real-world chaotic, unpredictable or quantum system, a deterministic algorithm produces a pseudo-random sequence.
Anthony, there are other posts that I've made where it is determined that the sequence is a de Bruijn sequence. What is most important about my work is the speed with which such a sequence can be generated; for 100 million digit de Bruijn sequence, my software produces same in less than 30 minutes. Also, while random is not computable, it is also true that random is biased from maximal disorder. Thanks for the reply.
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