On Wikipedia, I read that neural network functions defined in the field of arbitrary real / rational numbers (along with algorithmic schemes and speculative "recursive" models) have more computing power than the computers that we use today. Of course, this was the Russian Wikipedia page (en.wikipedia.org), and this may be incorrectly proved, but this is not the only source of such rumors.
Now what I really don’t understand is how is the line rewriting machine (NNs are the same as rewriting machines, just like Turing machines, only different programming languages) are more powerful than universal U machines?
Yes, the descriptive tool is really different, but the fact is that any function of this class can (easily or not) be turned into a legal Turing machine. Am I mistaken? Skip something important?
What is the reason that people say this? I know that the phenomenon of unsolvability is widely recognized today (although it is not always proven according to what I read), but I really do not see the least likelihood that NN will be able to solve this particular problem.
Add-in: Not consistently proven according to what I've read- I meant that you can take a look at the articles of A. Zenkin (Russian mathematician) after the mid-90s, where he convincingly postulates the fallacy of G. Cantor's concepts, including transfinite sets, uncountable sets, the diagonalization method ( the method used in the proof of Turing's unsolvability) and, possibly, others. Even Goedel's incompleteness theorems were proved in the right way only in the 21st century .. To just get Zenkin involved, I don’t know how widespread this knowledge is in the CS community, so forgive me if that looked silly.
Thank!
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