Τετάρτη, 1 Αυγούστου 2012

Finally it has been proven!

I had the impression that the Church-Turing thesis has not been proven, but a recent posting to the Arxiv server claimed otherwise. In partricular, Nachum Dershowitz and Evgenia Falkovic in their extended abstract entitled "A Formalization and Proof of the Extended Church-Turing Thesis" claim that they offer a proof of the Extended Church-Turing Thesis: Every effective algorithm can be efficiently simulated by a Turing machine. Interestingly, this proof uses the notion of classical algorithm which is a time-sequential state-transition system, whose transitions are partial functions on its states. But obviously, this is not an algorithm but something that someone calls a classical algorithm. Now if one has a deep desire to prove the Church-Turing thesis, then she can formulate and prove it inside Eff, that is, the effective topos (see Categorical Logic and Type Theory, p. 402)! In a nutshell, no I don't think this paper is a proof of the CTT.

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