One does not simply develop a coin where the proof of work is a general purpose problem solver. It would be very useful if that could be done, but as far as I know no one has found such a proof of work algorithm. It would have to be expensive to compute, with difficulty adjustable over a large range of values, easy to verify and capable of being tied to the hash of a specific block in the chain.
I think it is not simple to do but it would be amazing.
My idea is to develop a system where anyone can submit problems to be solved the submission must follow specific rules / language.
We need a verification procedure , the problem must be difficult to compute , more than the verificability , well defined for a parallel solver.
The difficulty over the time pheraps can be solved simply by the fact the system solve first simple instances of the problem because are more easy.
We have to find a way to tie to a specific block , etc...
OK , I am optimistic on solving these issues , the problem is how can we compare different problems which others? If I spent a lot of computational power in solving an instance I1 of a problem P1 this must be a of different value from solving an instance I2 of problem P2 and the reward must be different .
We can adjust the reward in automatic on how many instances of the problem are solved during the time in the network such that the system can change how much computational power give to every problem.
Another big problem I see is how to choose which problems to solve , how the system can select "useful" problems? We can submit absolutely useless problems well suited for the techincism of the system . How can the system choose the best problems ? There can be relatively simples and usefull problems and others relatively difficult and useless . Pherhaps this is too much.
I am very interested in developing a system in this direction , it would be very interesting to see discussions on this direction .