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04:26 < bsm117532> Eliel: yes that's one form of aggregation, see the "proofs of proofs of work" paper.
04:29 < Eliel> bsm117532: wouldn't a transaction chain work? Where individual transactions are chained and when you happen to find a low hash for one, that then becomes something kind of like a block.
04:29 < bsm117532> The loss of accuracy prevents its use for lots of things though.  The smallest hash in the chain won't change for roughly T time, where T is the age of the chain.  (You have to roughly double the hashpower*time to find a new smallest hash)
04:30 < bsm117532> Also if multiple miners are contributing to creating this smallest hash, you want to be able to have that data to decide compensation for them.
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07:52 < surae> any known work on partial transaction confirmations?
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08:58 < fluffypony> surae: partial as in?
08:59 < surae> well, the aggregatable idea above is sort of en route to what i'm thinking about
09:03 < surae> my shower thought was a scheme for collaborating on block verification, so if 2-of-3 or m-of-n miners together have a complete copy of the blockchain, they can collectively post a block and share reward
09:06 < surae> if miners X, Y, and Z each have about 2/3 of the blockchain and they bundle some txns into a "block..." such that for any one txn in the block, if X and Y together have a complete history of the txn, but Z is missing some of it,  or any 2-of-3...
09:08 < surae> then maybe they can build a merkle tree satisfying some difficulty target in order to earn the right to post the block to the blockchain. or something along those lines
09:09 < surae> similarly, miners without a fully copy of the blockchain would be forced to collaborate with each other while verifying blocks before relaying them or adding them to their local copy of the blockchain
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16:04 < bsm117532> surae: that's kind of the idea...if work can be aggregated, it could be done at the tx level or (some form of sub-block) level.  Miners could collaborate to produce the target PoW.  This could help decentralize mining, allow sub-chains/shards to be merge-mined, and a number of other interesting things.
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16:07 < gmaxwell> "Miners could collaborate to produce the target PoW."
16:07 < gmaxwell> 20:23 < gmaxwell> because you like progress and parties with the highest hashrate to solve all the blocks?
16:08 < bsm117532> I don't understand your comment.
16:08 < gmaxwell> Clearly.
16:09 < gmaxwell> bsm117532: imagine for a moment that you have your perfect cumulative proof of work.
16:09 < gmaxwell> where you can accumulate up single hashes and get a resulting POW with work equal to the sum of the hashes that went in.
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16:11 < gmaxwell> Now you, sipa, and I are miners.   Lets say 100,000 hashes are required to make a block.  Now say I have 40 hashes per second power, and you and sipa each have 30.
16:12 < sipa> gmaxwell is clearly using ASICBOOST
16:12 < gmaxwell> I could keep my solutions private and I will mine ~all the blocks.  Or alternatively, you and sipa could collude by sharing your solutions and I will mine none of them.
16:12 < gmaxwell> Cumulative work results in progress:  Faster wins, rather than fast hash improved odds proportional to their fastness.
16:14 < gmaxwell> s/rather than fast hash/rather than fast has/
16:14 < gmaxwell> E.g. I should win 40% of the blocks, not 100% (or 0%) in that example.
16:16 < bsm117532> Well that would be a bad way to organize it clearly.  I was mentioning tx level mining.  Block-builders could be solely aggregators, and different entities than miners.
16:16 < bsm117532> In other words, miners must be forced to share.  Selfish mining bad.
16:17 < gmaxwell> Because they're nice guys?  Why don't I spin up two identities Greg and Greg'  and greg' makes transactions and doesn't share them except with Greg?
16:17 < sipa> forcing miners to cooperate seems to remove the permissionless of mining
16:18 < bsm117532> Dunno.  I'm clearly not making a proposal yet.  Just wondering whether "aggregatable PoW" is a useful concept.
16:20 < gmaxwell> I'm sure it's useful for some thing. For POW purposes itself not so much perhaps.
16:20 < gmaxwell> We give an aggregate POW in the sidechains paper.
16:20 < bsm117532> gmaxwell: I would expect that to be common.  Block reward has to be removed.  Block aggregators wouldn't be incentivized, and the PoW payout would be in the individual mined txns.
16:20 < gmaxwell> but for many purposes the progress breaks it.
16:21 < bsm117532> gmaxwell: oh?  In reorg proofs?
16:22 < bsm117532> Really, Bitcion IS aggregated PoW, it just takes O(n) to verify.
16:23 < bsm117532> O(1) would be cool and could be used in new ways.
16:24 < sipa> but Bitcoin's aggregated PoW does more
16:24 < sipa> it's not only aggregating, it's also committing to the non-aggregated version
16:24 < sipa> if you can retain that property, i think you may be right
16:24 < sipa> but i also think that might be theoretically impossible in an O(1) construction :)
16:25 < gmaxwell> bsm117532: bitcoin like pow can be verified in ln(n), if you have the right commitments.
16:26 < gmaxwell> which is what the sidechains paper describes.
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17:01 < surae> @gmaxwell Your 10,000 hash example: there is a third option, where you have 40h/s, and sipa and bsm117532 have 30 h/s, where sipa and bsm start a pool...
17:01 < surae> and i don't quite follow how your argument isn't a criticism of pools
17:04 < surae> i think one good criticism of the idea is this
17:05 < gmaxwell> surae: I gave that example too.
17:05 < gmaxwell> "Or alternatively, you and sipa could collude by sharing your solutions and I will mine none of them."
17:05 < gmaxwell> surae: bitcoin pools don't have this property.
17:06 < gmaxwell> Bitcoin mining is progress free (at least on a single block basis)
17:06 < surae> ah, i thought you were referring to collusion by this accumulated hashing concept
17:06 < sipa> surae: in Bitcoin, a majority hashrate can collude
17:06 < gmaxwell> Yes, via agrregate proof of work. But that isn't what bitcoin pools do.
17:06 < sipa> but in a world where PoW has progress, the _highest_ hashrate can always win, even if it is not a majority
17:07 < gmaxwell> or the highest collusion, even if it is not a majority.
17:08 < surae> so, if you can make a continuous amount of progress, like a slider bar, i can see where you are going with that, and if the progress is discrete or atomic, you may as well be back to the usual block system
17:10 < bsm117532> sipa: commitments are easy to add to anything.
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17:10 < sipa> bsm117532: not if you still need to show all the originals in order to prove their correctness :)
17:11 < sipa> then you're back to an O(n) proof
17:11 < bsm117532> Commitments are easy to aggregate ;-)
17:11 < bsm117532> But yeah I see your point
17:11 < sipa> anyway, have a look at the "proofs of proof of work" work if you're not familiar with it
17:12 < sipa> (see what i did there? proofs proof, work work?)
17:12 < surae> hat tip
17:13 < sipa> surae: bitcoin mining has 0 progress
17:13 < bsm117532> I'm familiar ;-)
17:13 < surae> well, it's a coin flip, success or fail
17:13 < sipa> surae: the amount of work you've done before has no effect on how long it will take you to create the next block
17:15 < surae> yeah, that's what i was trying to get at
17:15 < surae> if we were to design a PoW system that has a progression instead of these discrete jumps
17:16 < surae> then the smallest discrete jump would be miner's new "target," like blocks would normally be, but rewards would occur every few successes instead of after a single success.
17:17 < bsm117532> smaller targets = more miners = more decentalization.
17:17 < surae> like halving, if you changed PoW to require two hashes that both satisfy a size requirement, you're still just flipping coins until a prescribed number of successes and then getting a reward
17:18 < surae> point being, I agree, the notion of progress breaks PoW pretty handily
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17:19  * bsm117532 finally gets gmaxwell's use of "progress"
17:20 < bsm117532> And here I thought it was just the opposite of congress.
17:22 < bsm117532> Well it seems I may get some time to work on braids again...and may be on the hunt for a PoW algorithm that makes sense for it...
17:22 < surae> braids as in category theory, or braids as in something else?
17:24 < surae> gmaxwell & sipa: the more precisely that hashrate determines the next block winner, the more often the largest miner wins, if hashrate *completely* determines the next block winner with no randomness, then largest miner always wins...
17:24 < bsm117532> braids as in organizing blocks into a directed acyclic graph (blocks can have multiple parents) instead of a chain. https://scalingbitcoin.org/hongkong2015/presentations/DAY2/2_breaking_the_chain_1_mcelrath.pdf
17:24 < surae> otoh, the less that hashrate determines next block winner, the more that smaller miners have a chance...
17:25 < surae> and hey, guess what, the exponential distribution has maximal entropy, so we want blocks to arrive in a poisson process, and not only that but a large number of coin flips is well-approximated as a poisson process...
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17:27 < bsm117532> More simulation and analysis: https://www.reddit.com/r/btc/comments/4su1gf/braiding_the_blockchain_32_min_qa_we_cant_remove/
17:27 < surae> which makes bitcoin's PoW impossible to improve, switching out hash functions or something silly like that can, at best, only improve how closely we can approximate the true block arrival rate as Poisson
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