Where the number of trials of a mechanism is bounded, it is sensible to engineer that mechanism to have such a small probability ϵ of failure that over all time we can discount the probability δ of it ever going wrong. So if there are at most 10⁹ trials and we are prepared to accept a δ=10⁻⁹ probability of failure over all time, this would suggest ϵ=10⁻¹⁸. If a blockchain has a good source of random numbers, this allows us to create many efficient mechanisms, including consensus, that are stochastically certain to work. A number of interesting challenges in formal reasoning arise.
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