I am no expert but the approaches in software can be of different types.
But the point nowdays is not to create mining software. But mining hardware ASICS.
So the question real is what trick can engineer do to make some efficient machine that can be produced TODAY with TODAY 's technology.
But that is not all, because if you make genious optimal chip it will burn in 1 second because there's so much transistors, it computes so fast so it overheats. In other words there are other considerations that are far more important. And that is before economic considerations.
If you want to understand, it's contest who makes better bow arrow, a race who hunts more dinosaurs.
we all know in the future there will be amazing breaktroughts. Just look at the new transistors that were announced currently there are CMOS, fet, finfet whatever.
In future there could be single atom transistors, or some epic new materials, or PET transistors up to 20 GHz
So I will tell you this, it is pointless to invent now some 'theoretical innovation" that will work only with today's technology, because tomorrow there could be whole different technology and the future chip will be efficient anyway, so everybody is going to throw your old today made chip with clever innovation to the trash anyway.
End of rant, so what can be doneSo logically you have many double sha hashers on chip. every one tries different nonce and changes it. The results can be AND and you don't need to compare different hashes individually just the AND result for zeroes. Successful solution is so rare so you can retry manually if you find it tthis way. But I'm sure engineers know this and maybe is not as genious idea.
hash collisionIt's possible to find recycled solution that after first SHA collides. But it's so difficult that nobody ever will do it. And even if, everybody on network will see it's recycled because the resulting hash will also collide. - stupid idea
study the equations. somebody can come up with good nonce guessers after studying sha equations. they don't have to be brilliant, just slightly better than random.
but I'm sure this will not the person think about the equations manually , or even use chalkboard or pen and paper. This way his brain will go retarded. The person must write some program that will do the difficult thinking.
bad nonce skippers - similiar you have good nonce planners, you can have bad nonce skippers. This is program who finds that some nonce sequence is worse and skips it. again this could be done from shasha equation, but just need to be slightly better than random ,excelent solution is not needed.