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Dec 25, 2014 at 10:52 comment added Ravi Andrew Bajaj But I see ways to work with solutions which do not at first have symmetry to get symmetry. For any two algorithms M1 and M2 that achieve this interpolation with the roles of 0 and 1 switched, we can have a third machine M3 that randomly choses a value printed by either M1 or M2.
Dec 25, 2014 at 9:41 comment added Bjørn Kjos-Hanssen Yes, some 0/1 symmetry would be nice...
Dec 25, 2014 at 8:53 comment added Ravi Andrew Bajaj I think the recursion in this algorithm is lovely, but I might add casually that arithmetic is not quite general enough. Neither the beginning, alternation, nor the end, randomness, are defined arithmetically, and likewise their interpolation would ideally exist outside of that fact. But even taking it as a fact of life... we also need symmetry between 0 and 1's, which might improve what you've shown us!
Dec 23, 2014 at 19:24 history answered Bjørn Kjos-Hanssen CC BY-SA 3.0