Alan Turing’s final publication concerns some numerical approximations for solving this problem, which he had earlier cited as a “number theoretic theorem” in his Ph.D. thesis. For 10 points each:
[10e] Name this unsolved problem that asserts that the real part of every non-trivial zero of the zeta function is one-half.
ANSWER: Riemann hypothesis [or RH]
[10m] The Riemann hypothesis is computationally equivalent to a Turing machine with 29 of these things halting. The input of the Busy Beaver function is the number of these things, which are denoted Q in the definition of a DFA.
ANSWER: states [or automaton states]
[10h] The equivalence arises from the DPRM theorem, which asserts that functions with this property can be written as Diophantine equations. Languages with this property are type 0 in Chomsky’s hierarchy, opposite regular languages at type 3.
ANSWER: recursively enumerable [reject “recursive”]
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