I can’t tell if there are any differences between non-recursively enumerable and uncomputable? what makes a language one or the other?
Is it safe to assume that all recursive languages are decideable or is it possible to have a undecideable language that’s recursive?
Are all recursively enumerable languages semi decideable (like halting problem) ?
please give examples if possible I’ve spent hours trying to wrap around these concepts and it just doesn’t feel right.
It seems that this article (https://arxiv.org/pdf/1312.4456.pdf) proposes that laws of physics are uncomputable (i.e they could not be reproduced on a computer), but I’m not sure about it.
In some part of the article it says:
If we expand the set of computational devices that we use to define computational complexity, then the consequences of the known laws of physics can in principle be elaborated in polynomical time on classical and quantum computers. If we restrict our attention to laws whose consequences can be evaluated in polynomial time, then the problem of finding concise expressions of physical laws is no longer uncomputable.
So, what is it saying? That laws of physics are uncomputable? That laws of physics could not be reproduced in a computer? That laws of physics could not be reproduced in any type of computer?
Also, in the conclusions it says:
This chapter reviewed how uncomputability impacts the laws of physics. Although uncomputability as in the halting problem arises from seemingly esoteric logical paradoxes, I showed that common and basic questions in physics have answers that are uncomputable. Many physical systems are capable of universal computation: to solve the question of whether such a system has discrete or continuous spectrum in a particular regime, or whether it is gapped or gapless, requires one to solve the halting problem. At a more general level one can think of the all scientific laws as providing concise, easily unpacked descriptions of obserbational and experimental data. The problem of finding the most concise description of a data set is uncomputable in general, and the problem of finding the most concise description whose predictions are easily evaluated is NP-complete
So, what can we conclude from this? Also, what does it exactly mean that “finding the most concise description whose predictions are easily evaluated is NP-complete”?