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From: ENGR@GSSI.MV.COM (Michael Furman)
Subject: Re: Style: multiple returns and relatives
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Date: Wed, 29 Nov 1995 00:12:42 GMT
References: <alberto.534.00162922@moreira.mv.com> <4950b5$qc9@alpha.pcix.com> <1995Nov2421.20.06.18267@silverton.berkeley.edu> <BLUME.95Nov25133647@zayin.cs.princeton.edu> <1995Nov2820.53.44.20508@silverton.berkeley.edu>
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In article <1995Nov2820.53.44.20508@silverton.berkeley.edu>, 
djb@silverton.berkeley.edu says...
>
>Matthias Blume <blume@zayin.cs.princeton.edu> wrote:
>> djb@silverton.berkeley.edu (D. J. Bernstein) writes:
>> > Provided that there are only finitely many inputs, and finitely many
>> > possible optimized programs to consider (``I don't want more than a
>> > gigabyte of output code, thank you''), the optimization problem is
>> > solvable.
>> Algorithms that solve the halting problem in bounded space (in
>> general) require time proportional to the size of the state space.
>
>You're missing the point. What I said is true even for Turing machines.
>
>We don't _have_ to figure out whether the optimized program halts. All
>we have do to is figure out whether it halts SOONER THAN THE ORIGINAL
>PROGRAM. That's utterly trivial to do, since the original program halts.

   It is true only for program without input (or with one pair: program and 
set of input parameters values). But in real life we do not need to optimize 
such program id it stops after small number of steps.
   If we have program with some space of possible inputs you will need some
number of steps for each element of that space. It is unsolvable for Turing 
machine and proportional to sum of N(s) where s is a state of input and N(s)
in number of steps until halt for this input. It is quite huge number - even 
if there is a garantee that N(s) is finite for each (crazy) input.
 


>
>---Dan

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