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Date: Fri, 3 Jul 2015 01:01:09 -0700
From: "Dennis E. Hamilton" <>
To: <>
Subject: RE: [PHC] Password hashing as a self-overwriting Turing machine

I made a serious understatement of the number of functions from 2^n to 2^n.  The problem of achieving Turing Completeness is even worse.
From: Dennis E. Hamilton [] 
Sent: Thursday, July 2, 2015 22:15
Subject: RE: [PHC] Password hashing as a self-overwriting Turing machine
Concerning claims for Turing Completeness, here is an argument to the contrary, below.
-   Dennis
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Now, the supposed total number of functions, Z -> Z for Z having 2^512 members is 
(2^512)^(2^512).  That’s a *lot* more than the number of functions that the 2^512 values in S can select among (and that assumes no duplicates arise in the selection).  
In addition, *all* of the (2^512)^(2^512) functions are computable.  Z is a finite domain, so the functions are enumerable. 
While nrOps complicates things, it is too small (not more than 8 bytes) to overcome this limitation and very large values of nrOps impact running time too much.  Also, too small values of nrOps don’t produce much transformation in the iterative BusyBeaver operations.
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