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Re: Validating that the implementation meets the spec for TM transition function [ best tape ]

From Ben <ben.usenet@bsb.me.uk>
Newsgroups comp.theory
Subject Re: Validating that the implementation meets the spec for TM transition function [ best tape ]
Date 2022-05-12 19:30 +0100
Organization A noiseless patient Spider
Message-ID <87h75u4n9j.fsf@bsb.me.uk> (permalink)
References (16 earlier) <t5hf7p$1kd4$1@gioia.aioe.org> <aYadnaAI4O_Z0uH_nZ2dnUU7_83NnZ2d@giganews.com> <t5htes$1hb4$1@gioia.aioe.org> <87sfpe4zo3.fsf@bsb.me.uk> <rNadnW2d0_Zm1uD_nZ2dnUU7-VfNnZ2d@brightview.co.uk>

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Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:

> On 12/05/2022 15:02, Ben wrote:
>> Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:
>> 
>>> You could think of a TM as a DFA that's been functionally enhanced to
>>> allow at each computation step
>>> i)  left/right (single) stepping of its input tape head
>>> ii) rewriting of the symbol under the tape head whereas a DFA is
>>> restricted to work with strictly right stepping of its "input tape
>>> head" so it only sees each character once (and so no concept of
>>> rewriting anything because it couldn't be reread anyway).
>> Though one used to talk about "transducer" DFAs where each edge of the
>> graph also had an output symbol.  This was not "written" anywhere but
>> the result was the concatenation of output after processing the input.
>> <cut>
>>> A) The DFA/TM termination conditions are a bit different.  A DFA halts
>>> naturally at the end of the input string, so it's fine (and typical)
>>> to have accept/reject states that are entered multiple times during a
>>> computation, i.e. those states aren't "final" states in the TM sense.
>>> A TM clearly needs some other way to explicitly indicate it's
>>> finished.  Typically (e.g. Linz) some TM states are designated "final"
>>> states that halt the TM - if it has accept/reject states those are
>>> final, so can only be entered once.
>> This is, as you say, typical.  But it's horrid!  Almost every author
>> seems to copy this ancient idea, but there's no need for the
>> complication.  A TM halts "naturally" when in a state that has no
>> defined transition for the current input.  
>
> From a programming perspective, I can see how that's a bit more
> convenient, but I don't like the idea that much - e.g. with an
> explicit halt state we can see it clearly on the state transition
> diagram (as one of the destination circles pointed to by arrows).  The
> alternative is having to inspect all the circles and identify those
> which are lacking some transition rule - that's lacking transparency
> in my opinion.
>
> (And if I identify such a state missing one or more arrows, am I to
> assume that's deliberate to create a halt condition, or does the
> author simply know that those conditions will never arise during
> execution, and was being "lazy"?)

When reasoning about termination, you have to consider halting in
non-final states, so I don't think it matters much. 

> So I'm thinking that an explicit halt state is maybe the most
> (conceptually) logical way to do it, and I like "conceptually
> logical".  To me the "no defined transition rule" seems like a kind of
> hack invented by a programmer to save a few lines of code!  (I've
> nothing against programmers of course, and if you teach people to
> program TM simulators, I can see the appeal of the idea.)
>
>> If you want and accept/reject
>> notion, then one can use a simple convention that the TM accepts if it
>> halts in a state with no defined transitions at all, but rejects if it
>> halts in state with defined transitions, none of which apply for the
>> current input.
>
> That seems (conceptually) awful to me!  I mean, where's the /logic/ in
> that, beyond making the programming task well defined for someone
> building a TM simulator?

The logic here that you have to consider the one case anyway (halting
because of no defined transition) and the second case is as explicit as
you'd like -- a state with no out-going arrows.  You can even agree to
draw double circles of these.

> Perhaps if I were more bold I might suggest your perspective could be
> overly shaped by your day to day job experience of teaching the
> /simulation/ side of the subject...  :)

That's possible.  Though one almost always just does this as a sketch.
The full details of a UTM are messy and don't really add much.

> For me, TMs are /mathematical/ constructs, used to discuss the nature
> of computation and limits of algorithms etc..  So naturally I like
> logical mathematical definitions.  For me, the weighting (out of 10)
> I'd apply to "making a programmer's job easier when coding a TM
> simulator" would be 0.  I mean, it's not /that/ hard whichever way we
> go.

I don't see it like that at all.  The reasoning about TMs is not made
any easier by the usual definitions unless, possibly, you insist that
the state transition function always maps every member of the tape
alphabet.

>> A few people prefer not to bother with accepting and rejecting states at
>> all, but instead just use the resulting tape.  For example, the TM is
>> deemed to have rejected the input if the tape is empty (i.e. contains no
>> non-blank symbols).
>
> Isn't there a problem here, in that now we can't actually tell when a
> computation is finished?  Say after 10^234829873473829 steps no output
> has been written - what does that signify?  OK, "nothing" is an
> answer, but then is this actually in line with our original intuitions
> which were concerning /finite/ algorithms?  This is a bit more like
> when TMs are /acceptors/ (recognisers?) rather than deciders, but even
> then, if a non-blank is written to the tape, it could be subsequently
> blanked out again, so its not really like an acceptor.

I don't see what you are getting at.  How is this different with
explicit final states?

There's no "we watch and see" here because, as you say, TMs are
mathematical constructs and a TM/input pair either denotes a finite
sequence of configurations or it does not.

> Perhaps something like "accept if 0 is ever written to the tape,
> reject if 1 is ever written"?  That would logially work I guess.

That would be weird.

> OK it's only now occured to me that you didn't say "..not to bother
> with *final* states.." or "..not to bother with *halting*..".  So I'm
> sure you meant having some explicit HALT action, followed by checking
> the tape to distinguish the halting reason - which makes perfect
> sense, and is maybe how I would have invented TMs (Terry-machines of
> course) :)

I'm not sure I follow.  Maybe you do see what I'm getting at?  A
decider, D, for a set, L(D), is a TM that always halts.  It therefore
computes a total function f_D: Σ* -> Σ*.  The accept/reject notion is
just a convention that can just as easily be defined as f_D(s) = ""
(say).  Similarly, a recogniser computes a partial function.

This is independent of the issue of how and when a TM halts, but my
preference is for both my suggestions.

-- 
Ben.

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Validating that the implementation meets the spec for TM transition function olcott <polcott2@gmail.com> - 2022-05-06 15:53 -0500
  Re: Validating that the implementation meets the spec for TM transition function Mr Flibble <flibble@reddwarf.jmc> - 2022-05-06 22:08 +0100
    Re: Validating that the implementation meets the spec for TM transition function olcott <polcott2@gmail.com> - 2022-05-06 16:25 -0500
      Re: Validating that the implementation meets the spec for TM transition function Mr Flibble <flibble@reddwarf.jmc> - 2022-05-06 22:29 +0100
        Re: Validating that the implementation meets the spec for TM transition function olcott <polcott2@gmail.com> - 2022-05-06 17:08 -0500
          Re: Validating that the implementation meets the spec for TM transition function Mr Flibble <flibble@reddwarf.jmc> - 2022-05-07 13:02 +0100
      Re: Validating that the implementation meets the spec for TM transition function Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2022-05-06 14:41 -0700
        Re: Validating that the implementation meets the spec for TM transition function olcott <polcott2@gmail.com> - 2022-05-06 17:02 -0500
          Re: Validating that the implementation meets the spec for TM transition function Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2022-05-06 15:36 -0700
            Re: Validating that the implementation meets the spec for TM transition function olcott <polcott2@gmail.com> - 2022-05-06 17:54 -0500
          Re: Validating that the implementation meets the spec for TM transition function Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2022-05-07 00:39 +0100
            Re: Validating that the implementation meets the spec for TM transition function olcott <polcott2@gmail.com> - 2022-05-06 18:54 -0500
          Re: Validating that the implementation meets the spec for TM transition function Ben <ben.usenet@bsb.me.uk> - 2022-05-07 01:54 +0100
            Re: Validating that the implementation meets the spec for TM transition function olcott <polcott2@gmail.com> - 2022-05-06 20:05 -0500
              Re: Validating that the implementation meets the spec for TM transition function Ben <ben.usenet@bsb.me.uk> - 2022-05-07 23:21 +0100
                Re: Validating that the implementation meets the spec for TM transition function Jeff Barnett <jbb@notatt.com> - 2022-05-07 19:57 -0600
                Re: Validating that the implementation meets the spec for TM transition function Richard Damon <Richard@Damon-Family.org> - 2022-05-08 07:34 -0400
                Re: Validating that the implementation meets the spec for TM transition function Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2022-05-08 05:11 -0700
                Re: Validating that the implementation meets the spec for TM transition function Richard Damon <Richard@Damon-Family.org> - 2022-05-08 14:20 -0400
                Re: Validating that the implementation meets the spec for TM transition function Ben <ben.usenet@bsb.me.uk> - 2022-05-08 19:59 +0100
                Re: Validating that the implementation meets the spec for TM transition function Ben <ben.usenet@bsb.me.uk> - 2022-05-09 03:14 +0100
                Re: Validating that the implementation meets the spec for TM transition function olcott <NoOne@NoWhere.com> - 2022-05-08 22:39 -0500
                Re: Validating that the implementation meets the spec for TM transition function Ben <ben.usenet@bsb.me.uk> - 2022-05-09 12:36 +0100
                Re: Validating that the implementation meets the spec for TM transition function Ben <ben.usenet@bsb.me.uk> - 2022-05-08 14:44 +0100
                Re: Validating that the implementation meets the spec for TM transition function Jeff Barnett <jbb@notatt.com> - 2022-05-08 11:08 -0600
                Re: Validating that the implementation meets the spec for TM transition function Ben <ben.usenet@bsb.me.uk> - 2022-05-08 19:27 +0100
                Re: Validating that the implementation meets the spec for TM transition function Richard Damon <Richard@Damon-Family.org> - 2022-05-08 15:22 -0400
                Re: Validating that the implementation meets the spec for TM transition function Mr Flibble <flibble@reddwarf.jmc> - 2022-05-08 20:30 +0100
                Re: Validating that the implementation meets the spec for TM transition function olcott <NoOne@NoWhere.com> - 2022-05-09 10:53 -0500
                Re: Validating that the implementation meets the spec for TM transition function Ben <ben.usenet@bsb.me.uk> - 2022-05-09 23:08 +0100
                Re: Validating that the implementation meets the spec for TM transition function olcott <NoOne@NoWhere.com> - 2022-05-09 17:32 -0500
                Re: Validating that the implementation meets the spec for TM transition function Richard Damon <Richard@Damon-Family.org> - 2022-05-09 20:31 -0400
                Re: Validating that the implementation meets the spec for TM transition function Ben <ben.usenet@bsb.me.uk> - 2022-05-10 01:37 +0100
                Re: Validating that the implementation meets the spec for TM transition function olcott <NoOne@NoWhere.com> - 2022-05-09 20:29 -0500
                Re: Validating that the implementation meets the spec for TM transition function Ben <ben.usenet@bsb.me.uk> - 2022-05-10 11:35 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape] olcott <NoOne@NoWhere.com> - 2022-05-10 19:12 -0500
                Re: Validating that the implementation meets the spec for TM transition function Jeff Barnett <jbb@notatt.com> - 2022-05-08 14:51 -0600
                Re: Validating that the implementation meets the spec for TM transition function olcott <NoOne@NoWhere.com> - 2022-05-09 10:18 -0500
                Re: Validating that the implementation meets the spec for TM transition function Ben <ben.usenet@bsb.me.uk> - 2022-05-09 23:14 +0100
                Re: Validating that the implementation meets the spec for TM transition function olcott <NoOne@NoWhere.com> - 2022-05-09 17:42 -0500
                Re: Validating that the implementation meets the spec for TM transition function Ben <ben.usenet@bsb.me.uk> - 2022-05-10 01:13 +0100
                Re: Validating that the implementation meets the spec for TM transition function olcott <NoOne@NoWhere.com> - 2022-05-09 20:28 -0500
                Re: Validating that the implementation meets the spec for TM transition function Richard Damon <Richard@Damon-Family.org> - 2022-05-09 23:34 -0400
                Re: Validating that the implementation meets the spec for TM transition function Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2022-05-10 00:24 -0700
                Re: Validating that the implementation meets the spec for TM transition function Ben <ben.usenet@bsb.me.uk> - 2022-05-10 11:31 +0100
                Re: Validating that the implementation meets the spec for TM transition function Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2022-05-10 03:46 -0700
                Re: Validating that the implementation meets the spec for TM transition function Ben <ben.usenet@bsb.me.uk> - 2022-05-10 12:23 +0100
                Re: Validating that the implementation meets the spec for TM transition function olcott <NoOne@NoWhere.com> - 2022-05-10 06:53 -0500
                Re: Validating that the implementation meets the spec for TM transition function Richard Damon <Richard@Damon-Family.org> - 2022-05-10 08:01 -0400
                Re: Validating that the implementation meets the spec for TM transition function Ben <ben.usenet@bsb.me.uk> - 2022-05-10 16:41 +0100
                Re: Validating that the implementation meets the spec for TM transition function Jeff Barnett <jbb@notatt.com> - 2022-05-10 11:56 -0600
                Re: Validating that the implementation meets the spec for TM transition function olcott <NoOne@NoWhere.com> - 2022-05-10 19:43 -0500
                Re: Validating that the implementation meets the spec for TM transition function Jeff Barnett <jbb@notatt.com> - 2022-05-10 20:49 -0600
                Re: Validating that the implementation meets the spec for TM transition function Mr Flibble <flibble@reddwarf.jmc> - 2022-05-10 19:01 +0100
                Re: Validating that the implementation meets the spec for TM transition function "dklei...@gmail.com" <dkleinecke@gmail.com> - 2022-05-10 11:59 -0700
                Re: Validating that the implementation meets the spec for TM transition function olcott <NoOne@NoWhere.com> - 2022-05-10 19:04 -0500
                Re: Validating that the implementation meets the spec for TM transition function Ben <ben.usenet@bsb.me.uk> - 2022-05-11 01:42 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-10 20:12 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2022-05-11 03:05 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-10 21:14 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2022-05-11 02:19 -0700
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-11 08:54 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2022-05-11 16:27 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-11 10:36 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2022-05-11 16:49 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2022-05-11 14:30 -0700
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-11 16:38 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2022-05-12 00:01 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-11 19:05 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2022-05-12 04:03 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-11 22:29 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-11 22:37 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-12 15:02 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2022-05-12 19:03 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-12 19:30 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-12 14:23 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Richard Damon <Richard@Damon-Family.org> - 2022-05-12 19:19 -0400
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2022-05-13 01:02 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Jeff Barnett <jbb@notatt.com> - 2022-05-11 23:13 -0600
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-12 00:43 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-11 04:02 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-10 22:07 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-11 13:40 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-11 09:02 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2022-05-11 16:09 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-11 10:29 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-11 20:35 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-11 15:12 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-11 22:54 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-11 17:02 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-12 02:00 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-11 20:37 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-12 02:49 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-11 21:49 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-12 14:45 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-12 10:31 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-12 21:20 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-12 15:33 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Mr Flibble <flibble@reddwarf.jmc> - 2022-05-12 21:36 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-12 16:28 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Mr Flibble <flibble@reddwarf.jmc> - 2022-05-12 22:33 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-12 22:02 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-12 16:14 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-13 00:18 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-12 18:22 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-13 01:10 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-12 19:58 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-13 02:54 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Richard Damon <Richard@Damon-Family.org> - 2022-05-12 22:09 -0400
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-12 21:41 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Mikko <mikko.levanto@iki.fi> - 2022-05-13 10:01 +0300
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-13 10:57 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Mikko <mikko.levanto@iki.fi> - 2022-05-13 19:06 +0300
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-13 11:54 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Mr Flibble <flibble@reddwarf.jmc> - 2022-05-13 13:38 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-13 11:07 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Mr Flibble <flibble@reddwarf.jmc> - 2022-05-13 17:14 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-13 12:03 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Mr Flibble <flibble@reddwarf.jmc> - 2022-05-13 18:09 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-13 12:15 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-13 17:26 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-13 12:07 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-13 19:45 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-13 13:57 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Richard Damon <Richard@Damon-Family.org> - 2022-05-13 15:04 -0400
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-13 14:15 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Richard Damon <Richard@Damon-Family.org> - 2022-05-13 15:40 -0400
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-13 14:58 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Richard Damon <Richard@Damon-Family.org> - 2022-05-13 16:24 -0400
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-13 15:33 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Richard Damon <Richard@Damon-Family.org> - 2022-05-13 17:25 -0400
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-13 16:48 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Richard Damon <Richard@Damon-Family.org> - 2022-05-13 18:05 -0400
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-13 20:12 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-13 14:28 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-13 21:58 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-13 16:12 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-13 23:57 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-13 17:59 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-14 01:00 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-13 19:09 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-14 01:21 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-17 13:17 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2022-05-14 01:54 -0700
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-14 04:13 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2022-05-14 03:30 -0700
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-14 08:51 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2022-05-14 11:38 -0700
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-14 13:54 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-14 13:15 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2022-05-14 11:37 -0700
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2022-05-14 19:47 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-14 20:15 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2022-05-14 12:52 -0700
                Re: Validating that the implementation meets the spec for TM transition function [ unlimited scalability ] olcott <NoOne@NoWhere.com> - 2022-05-13 16:43 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ unlimited scalability ] Ben <ben.usenet@bsb.me.uk> - 2022-05-13 23:58 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ unlimited scalability ] olcott <NoOne@NoWhere.com> - 2022-05-13 18:03 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Jeff Barnett <jbb@notatt.com> - 2022-05-13 15:06 -0600
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-13 16:16 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Jeff Barnett <jbb@notatt.com> - 2022-05-13 17:48 -0600
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-13 19:06 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Jeff Barnett <jbb@notatt.com> - 2022-05-13 19:58 -0600
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-13 22:39 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Jeff Barnett <jbb@notatt.com> - 2022-05-13 19:48 -0600
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-13 11:00 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Richard Damon <Richard@Damon-Family.org> - 2022-05-13 12:08 -0400
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Ben <ben.usenet@bsb.me.uk> - 2022-05-13 17:27 +0100
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] olcott <NoOne@NoWhere.com> - 2022-05-13 12:10 -0500
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Richard Damon <Richard@Damon-Family.org> - 2022-05-13 13:20 -0400
                Re: Validating that the implementation meets the spec for TM transition function [ best tape ] Richard Damon <Richard@Damon-Family.org> - 2022-05-11 22:07 -0400
                Re: Validating that the implementation meets the spec for TM transition function olcott <NoOne@NoWhere.com> - 2022-05-10 21:06 -0500
                Re: Validating that the implementation meets the spec for TM transition function Ben <ben.usenet@bsb.me.uk> - 2022-05-11 00:11 +0100
                Re: Validating that the implementation meets the spec for TM transition function olcott <NoOne@NoWhere.com> - 2022-05-10 19:41 -0500
                Re: Validating that the implementation meets the spec for TM transition function olcott <NoOne@NoWhere.com> - 2022-05-10 06:53 -0500
                Re: Validating that the implementation meets the spec for TM transition function olcott <NoOne@NoWhere.com> - 2022-05-07 21:04 -0500
                Re: Validating that the implementation meets the spec for TM transition function Richard Damon <Richard@Damon-Family.org> - 2022-05-08 07:30 -0400
                Re: Validating that the implementation meets the spec for TM transition function Ben <ben.usenet@bsb.me.uk> - 2022-05-08 14:46 +0100
                Re: Validating that the implementation meets the spec for TM transition function olcott <NoOne@NoWhere.com> - 2022-05-09 10:19 -0500
        Re: Validating that the implementation meets the spec for TM transition function Ben <ben.usenet@bsb.me.uk> - 2022-05-07 01:22 +0100
          Re: Validating that the implementation meets the spec for TM transition function olcott <polcott2@gmail.com> - 2022-05-06 19:38 -0500
            Re: Validating that the implementation meets the spec for TM transition function Ben <ben.usenet@bsb.me.uk> - 2022-05-07 02:01 +0100
              Re: Validating that the implementation meets the spec for TM transition function olcott <polcott2@gmail.com> - 2022-05-06 20:22 -0500
                Re: Validating that the implementation meets the spec for TM transition function Ben <ben.usenet@bsb.me.uk> - 2022-05-07 23:30 +0100
          Re: Validating that the implementation meets the spec for TM transition function Ben <ben.usenet@bsb.me.uk> - 2022-05-07 02:04 +0100
            Re: Validating that the implementation meets the spec for TM transition function olcott <polcott2@gmail.com> - 2022-05-06 20:26 -0500
            Re: Validating that the implementation meets the spec for TM transition function Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2022-05-07 05:00 -0700
              Re: Validating that the implementation meets the spec for TM transition function Ben <ben.usenet@bsb.me.uk> - 2022-05-07 23:31 +0100
                Re: Validating that the implementation meets the spec for TM transition function olcott <NoOne@NoWhere.com> - 2022-05-07 18:36 -0500
                Re: Validating that the implementation meets the spec for TM transition function Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2022-05-08 02:39 -0700
                Re: Validating that the implementation meets the spec for TM transition function [ priorities ] olcott <NoOne@NoWhere.com> - 2022-05-08 17:21 -0500
  Re: Validating that the implementation meets the spec for TM transition function Mikko <mikko.levanto@iki.fi> - 2022-05-07 11:06 +0300
    Re: Validating that the implementation meets the spec for TM transition function olcott <polcott2@gmail.com> - 2022-05-07 11:14 -0500
      Re: Validating that the implementation meets the spec for TM transition function Mikko <mikko.levanto@iki.fi> - 2022-05-08 11:57 +0300
        Re: Validating that the implementation meets the spec for TM transition function olcott <NoOne@NoWhere.com> - 2022-05-09 10:35 -0500

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