Church-Turing Thesis

Equivalently, it holds that a function is recursive if and only if it is computable.

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Notoriously, quantum computation shatters complexity theory, but is innocuous to computability theory.

Yet several works have shown how quantum theory as it stands could breach the physical Church-Turing thesis.

is a (mostly informal) statement about the nature of computability.

It roughly asserts that there is, up to equivalence, only one single universal concept of computability.

These traditional algorithms are known also as classical or sequential.

In the original thesis, effectively computable meant computable by an effective classical algorithm.83), but they are type-II computable (Weihrauch-Zhong 01, Weihrauch-Zhong 02, Weihrauch-Zhong 06).For more on this see at for a general account and (Waaldijk 03) for a more formal account emphasizing the role of intuitionistic/constructive mathematics.My hunch is the author is mixing in "higher-order" logic "version of Church-Turing" into their argument.Which is basically "cheating", switching to an effectively different question without making things clear. This is basically opaque to my mere MA-level maths.All links about things talked in this talk just seem to lead to other texts and such by this author.Might not be a good sign but maybe it's just a very hard to grasp realm.He does in fact provide at least one counterexample (around in the video).One is the real-number GCD algorithm; basically the same as Euclid's standard GCD algorithm, but with real numbers. It's one of those talks that seems to talk about things I know but then immediately jumps to theories and definitions I have never heard of."Sequential algorithms were axiomatized in 2000" - This "axiomization" was apparently performed by the author of the talk, my Googling says.

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