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Re: Re: Trust question (fwd)
I don't know where to reply to Ed, since he is posting this widely.
Ed Gerck, <egerck@laser.cps.softex.br>, writes:
> That said, supose you have a Turing [1] machine for each statement.
> The three machines have fully independent initial states.
>
> Take now one machine at a time. Represent each A, B and C as states
> in that machine (which has also other states such as D, E, F..) and
> take x and y as conditions that relate states A, B and C according to
> each statement (also including arbitrary conditions z, u, v, w, etc
> for connections between other states). Make sure that A, B and C have
> no connection in their respective initial states, which are otherwise
> random.
This doesn't make sense. A Turing machine has a tape, internal states,
and a transition table giving the next state given the current state
and the current symbol on the tape.
"Represent each A, B and C as states in that machine..." We can define A,
B, C as states within the machine. That part is trivial; we can label
states any way we want.
Now we are to "take x and y as conditions that relate states A, B and
C according to each statement". What does that mean? Is this part of
the state transition table? B transitions to C when it sees something
(x?) on the tape? I don't see any way to represent this instruction
in a Turing machine transition table.
"Make sure that A, B and C have no connection in their respective
initial states." Again, what does this mean? We have A, B and C as
three different states within our TM. Or are you now talking about the
three different TMs as A, B, and C? That is very confusing terminology.
If the latter, what does it mean that the three TMs have no connection
in their respective initial states? They are three separate TMs, so
of course there is no connection between them.
> After each machine runs, compare the final states for each A, B and C
> in all three machines, two at a time. Then, change all initial
> conditions in all possible variables, respecting the restraints and
> run again. Do that enough times. From all such comparisons you have
> the answers to the binary comparison requested.
What does it mean to compare the final states? A TM identifies one of
its states as the halt state. This will always be the final state of the
machine, so no information will come of comparing final states. Or are
you referring to the contents of the output tape? You have said nothing
about what should be put on the tapes, or how they should be interpreted.
I can't make heads or tails out of this TM business. I don't know if
Ed means to be taken literally or if this is meant to be a metaphor
or approximation.
> Then, you see that the problem IS determinate. The fact that one may
> not have its solution now that does not mean that a solution does not
> exit of course. Does not mean that one cannot calculate it in closed
> form either.
I and others complained to Ed on sci.crypt about his use of a quasi
mathematical notation to represent trust relationships. I have to make
the same complaint here about this attempt to use the theory of Turing
machines to draw some conclusions about trust. It does not appear
to be using standard terminology, there is fuzziness about conditions
and connections, and the whole discussion doesn't end up communicating
anything when you look at it in detail.
Hal Finney
hal@rain.org
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