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Nxt developer & smartcontract.com cofounder Alexander Chepurnoy will give a detailed description of an Nxt-like proof-of-stake consensus algorithm & possible known improvements of it. Different attacks on the algo (short & long private forks, history attacks, and the very famous Nothing-at-Stake attack) will be considered along with simulation results. An innovative approach for proof-of-stake consensus improvement will then be presented. Finally, after a brief overview of some formal models around blockchain properties being built, an ultra-compact cryptocurrency engine for hackers within just 4K lines of Scala code will be presented!