How useful is Turing completeness? are neural nets turing complete?

Question

While reading some papers about the Turing completeness of recurrent neural nets (for example: Turing computability with neural nets, Hava T. Siegelmann and Eduardo D. Sontag, 1

Answer 1

It is almost always nice to know which class in the Chomsky hierarchy your system is. This is especially important in the more constricted classes, like regular languages / finite automata vs context-free languages. Also having the skill to recognize which class your the problem you are trying to solve is in is also important, otherwise one might try to do silly things like parsing HTML or XML with regular expressions only, which is impossible.

Having the knowlegde that your formalism or system is turing complete makes a statement that you can build whatever you want with it. It does not say anything about practicality, just the possibility or impossibility of solving problems. This is painfully true when considering turing tarpits, but there is also many turing complete systems which are specifically made for niche purposes that no one should ever dream of using for general purpose work in a production setting.

In short, good knowledge of the Chomsky hierarchy will help you out in very many situations, not only for choosing the right type of parser; regexp, pushdown, CFG or more powerful, but also for choosing the right type of machine or formalism for expressing processes in general.