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Questions related to combinatorics and discrete mathematical structures

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Do most bitstrings expand if they halt when executed by a Universal Turing machine?

Well, ... several (different!) scenarios: I assume that U is a (fixed) UTM, you give it a string s = (TM,input), U(s) = TM(input) = either a finite output "f" or else DIS, the TM does not halt. Add …
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