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From: ttobler@unislc.slc.unisys.com (Trent Tobler)
Subject: Re: Style: multiple returns and relatives
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Date: Fri, 1 Dec 1995 18:23:03 GMT
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Scot Dyer (swd@cse.unl.edu) wrote:
: djb@silverton.berkeley.edu (D. J. Bernstein) writes:

: >Remember, we're starting from a working program W that always halts.
: >Given another program P, and given an input, we want to know if P
: >runs _more quickly_ than W and produces the same output. This is
: >completely straightforward to test.

: Ha ha hahaha.  You're right, of course.  This is, however, one of the
: very good reasons why we should model computers mathematically as though
: they were infinite.  For example, how many different 1 gigabyte or less
: outputs are there?  (To be _practical_, the answer is "infinitely many.")

Joining this thread with a previous thread, ... it may be that on quantum
computers, the '1 gigabyte' outputs may not necessarily be 'infinitely many'.
Given that we can actually build quantum computers with 1 gigabyte of
processing units, it very well could be possible to analyze all 2^(2^20)
possible outputs simultaneously.  My point being, I guess, is that because
real computers are not Turing computers, there may be some innovative or
creative way to create a machine or program that answers "What is the
shortest/fastest program equivilant to program X running on machine Y = some
FSM+tape(N)", or "Does this program halt for every input?  Does it loop for
every input?"...  Theoretically, it is possible.  To discount the possiblility
because of current practical limitations seems a little premature..

--
  Trent Tobler - ttobler@unislc.slc.unisys.com
