```Date: Jan 18, 2013 7:13 PM
Author: Graham Cooper
Subject: Re: The MYTH of UNCOMPUTABLE FUNCTIONS

On Jan 19, 5:40 am, George Greene <gree...@email.unc.edu> wrote:> On Jan 12, 4:48 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:>> > Turing's Halt Proof clearly proves that>> > HALT( program, input )  --> [yes/no]>> > is not a PURE FUNCTION!>> It's not OUR fault if you don't understand the proof.> What the proof actually "clearly" proves ("clearly"> in scare-quotes because it is unfortunately NOT clear to YOU)> is that HALT( , ) is not A TURING MACHINE.>> >> How do you define "pure function"?> > the output is determined by the input alone>> In the case of HALT ( , ), the output IS determined by the input> alone.  For every TMprogram, it either halts or it doesn't.> ON EVERY input.  Given the program,  THE INPUT ALONE determines> that truth-value.  This is just a fact about TMs.  Given this> fact, it will follow that Halt( , ) is not a TM.  But that does> not stop it from being a pure function -- it's DEFINED as a pure> function, so that is not even open to dispute.>Assume a process exists that runs any other process and ADDS 1.Run 2 of these processes and cross the inputs.Each process has it's one required argument.P_1(P_2)P_2(P_1)Neither can terminate - DEADLOCKAccording to you, this proves the  SUCCESSOR FUNCTION  is un-computable!STEP 1:  ASSUME P HALTS GIVEN AN INPUT PROCESS THAT HALTSSTEP 2:  P_1 HALTS  (from 1)STEP 3:  P_2 HALTS  (from 1)STEP 4:  P_1(P_2)  should HALT  (from 2 & 3)CONTRADICTONTHEREFORE  ADDING 1 TO A PROCESS' RESULT IN UN-COMPUTABLES: if stops(S) gosub SG. GREENE:  this proves stops() must be un-computable!G. Cooper  (BInfTech)--http://tinyURL.com/BLUEPRINTS-MATHEMATICShttp://tinyURL.com/BLUEPRINTS-HYPERREALShttp://tinyURL.com/BLUEPRINTS-QUESTIONShttp://tinyURL.com/BLUEPRINTS-POWERSEThttp://tinyURL.com/BLUEPRINTS-THEOREMhttp://tinyURL.com/BLUEPRINTS-PROLOGhttp://tinyURL.com/BLUEPRINTS-FORALLhttp://tinyURL.com/BLUEPRINTS-TURINGhttp://tinyURL.com/BLUEPRINTS-GODELhttp://tinyURL.com/BLUEPRINTS-PROOFhttp://tinyURL.com/BLUEPRINTS-MATHShttp://tinyURL.com/BLUEPRINTS-LOGIChttp://tinyURL.com/BLUEPRINTS-BRAINhttp://tinyURL.com/BLUEPRINTS-PERMhttp://tinyURL.com/BLUEPRINTS-REALhttp://tinyURL.com/BLUEPRINTS-SETShttp://tinyURL.com/BLUEPRINTS-HALThttp://tinyURL.com/BLUEPRINTS-P-NPhttp://tinyURL.com/BLUEPRINTS-GUThttp://tinyURL.com/BLUEPRINTS-BBhttp://tinyURL.com/BLUEPRINTS-AI
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