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Right now, every node in a Proof of Work system, solves the POW puzzle independently.

Is there any concept of group proof of work, where everyone in the group needs to solve part of the puzzle.

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I believe any function that was not independent would have progress-- a miner with 3x the hashing speed would be first more often than 3x the time. When applied to POW consensus, progress is very bad for decentralization because it directly increases the income/influence of centralized parties/collaborations.

An example of one of these progress bearing non-independent mining constructions would be instead of finding 1 threshold meeting solution for your block, find 10 nonces that give you 10 threshold meeting solutions.

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Describing PoW as a puzzle is not the best of analogies. It is more accurate to describe as a search (i.e. miners are searching for a Proof of Work which satisfies a condition).

While the PoW search can be parallelized, it is not possible that a particular solution can be pieced together from the parallelized work. A searcher either finds the whole the solution or none of the solution.

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  • It seems to me what OP is asking about is a group of nodes essentially acting as one node (in the sense of the reward) but divvying up search locations for a nonce to search independently in hopes that one of them will find it before other nodes not in the collusion. Think, a 'tribe' of nodes that then shares earnings. – Prince M Jun 26 '18 at 23:42
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The concept is a commonly referred to as divide and conquer. Sorting a list can be done similar. Divide the list into 2 smaller parts and merge the two. A list of one item is sorted. Merging the 2 results in a fast efficient sorting algorithm. Something similar can be done on proof of work. Divide the work to be proven over many small parts and let them all proof a little bit of work. Then merge these small proofs into a larger proof or work. (It could both reduce energy usage and solve scalability of bitcoin.)

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  • Proof of Work solutions are not composable. Any Bitcoin block candidate that differs even by one byte is simply a different solution. – Murch Jul 8 at 12:06
  • @Murch Ok. Hashing seems not composable. I assumed it was similar to merging two compatible chains. But that's what the difficulty seems to be used for. (More resources equals more difficult.) Even if it would be composable you would be in a race for more resources. – Wouter Jul 8 at 18:42
  • It's not clear to me what you mean with "merging two compatible chains". The best chain has exactly one block at each height, and if there are multiple competing chaintips, each node will consider the one they saw first to be the best until one of the two pulls ahead. – Murch Jul 8 at 19:33
  • Compatible as in: A chain that has valid transactions (maybe no block rewards) that would otherwise just have to be added to main chain. So no double spending etc… but still has a sufficient amount of pow The next block in the main chain would just have a reference to the previous block and this chain that needs to be merged. But for the total amount of energy with respect to the total amount of work done there is not really a difference.(of course this is not how Bitcoin works but for a POW it could be any directed acyclic graph. Of which a chain is just the easiest. – Wouter Jul 8 at 22:31

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