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Generally, blockchain "mining" requires a problem that is hard to solve, easy to verify. If I understand it correctly, the genome sequencing problem is hard to solve, hard to verify.

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No, a given assembly is easy to verify. The complexity in actual application comes from the fact that performing the sequencing part (the biological/mechanical part) again will yield a different assembly due to biological and technical variability. Another complexity comes from the fact that you can define different measures of “goodness” (and hence optimality), depending on which errors you model.

But from a computational standpoint, sequence assembly (using a given error metric) is simply NP-hard.

What you just said is the "definition" of NP problems which is why I had it in my question to begin with. Even if genome sequencing is not a good problem for mining. There are plenty of other scientific problems that are. Yet mining today is not tackling any of them :/

The miner's identity (more or less) has to be one of the inputs to the problem, so that everyone is actually working on a different problem and you can't "steal" a block just by broadcasting another person's solution faster and wider.

Maybe there could be useful problems with this property, but it's not trivial to find them.

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