tag:blogger.com,1999:blog-1039373877769915493.post6042313497789396680..comments2020-11-03T05:08:07.582-06:00Comments on Distributed Computing and Societal Networking: Provably Probable Is Better Than Probably ProvableJim Duttonhttp://www.blogger.com/profile/06293311386552614976noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-1039373877769915493.post-24520000969638353992011-01-28T13:39:30.747-06:002011-01-28T13:39:30.747-06:00Carlos, you are exactly right. It's about the ...Carlos, you are exactly right. It's about the ability of the faulty process to predict the future states of the non-faulty ones. In fact, there are a number of practical solutions to the asynchronous BA problem that involve encryption. However, if the communication model is asynchronous (no bound on the delivery times of messages) all these solutions MUST be probabilistic. Lynch, et el, prove it in the paper I referenced.<br /><br />Your last question is something I plan to revisit in a future post. Briefly, if random means unpredictable, then truly random means unpredictable to everyone and everything. The question of whether such a phenomenon exists in the universe gets deep very quickly, touching on quantum physics, the foundations of logic, and theology, all of which I have only a hobbyist familiarity with.Jim Duttonhttps://www.blogger.com/profile/06293311386552614976noreply@blogger.comtag:blogger.com,1999:blog-1039373877769915493.post-46841689520962202582011-01-27T13:56:53.787-06:002011-01-27T13:56:53.787-06:00With the coin toss, The Faulty One can not thwart ...With the coin toss, The Faulty One can not thwart agreement because he can not predict how the others will vote. What it comes down to is prediction. If the other voters were to come up with their own algorithm and not tell the otherwise-omniscient Faulty One, that would also prevent prediction and thwart the malicious plan. The secret algorithm could be deterministic or not. Therefore it is not probabilistic algorithms per se that save the day, but insufficient predictive ability.<br /><br />Random means unpredictable, but unpredictable to whom?Carlos Rumbautnoreply@blogger.com