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Dec 9, 2015 at 22:46 comment added SDL That's the idea. For example, the High-Value-Hash Highway (bitcointalk.org/index.php?topic=98986.msg1083483#msg1083483) allows one to build a cumulative proof-of-work, over the whole chain, but its size is not bounded by the logarithm of the difficulty, but bounded by the logarithm of the chain length.
Oct 27, 2015 at 17:34 comment added John Tromp Your original description suggested to me that you intend for many consecutive improvement steps. Otherwise "comparing the difficulty of two competing chains is reduced to comparing the difficulties of two blocks" makes no sense to me, as the PoW of the blocks you compare would need to be cumulative over the whole chain.
Oct 26, 2015 at 16:28 comment added SDL It's still progress-free, because each PoW A(i) is progress-free, and each block would need a single proof step (from A(n) to A(n+1)) and not many steps.
Oct 24, 2015 at 21:59 history edited John Tromp CC BY-SA 3.0
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Oct 23, 2015 at 15:51 history answered John Tromp CC BY-SA 3.0