ONT Re: Differential Analytic Turing Automata

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DATA.  Note 17

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We have been conducting the differential analysis
of the logical transformation F : [u, v] -> [u, v]
such that F : <u, v> ~> <((u)(v))>, ((u, v))>, and
this means starting with the extended transformation
EF : [u, v, du, dv] -> [u, v, du, dv] and breaking it
into an analytic series, EF = F + dF + d^2.F + ..., and
so on until there is nothing left to analyze any further.

As a general rule, one proceeds by the following stages:

1.  EF      =  [d^0]F + [r^0]F

2.  [r^0]F  =  [d^1]F + [r^1]F

3.  [r^1]F  =  [d^2]F + [r^2]F

4.  ...

In our analysis of the current transformation F,
we carried out Step 1 in the more familiar form
EF = F + DF, and we have just reached Step 2 in
the form DF = dF + rF, where rF is the residual
term that remains for us to examine next.

NB.  I'm am trying to give quick overview here,
and this forces me to omit many picky details.
The picky reader may wish to consult the more
detailed presentation of this material in the
following ur-neighborhoods:

Jon Awbrey, "Differential Logic and Dynamic Systems"

DLOG D.  http://stderr.org/pipermail/inquiry/2003-May/thread.html#478
DLOG D.  http://stderr.org/pipermail/inquiry/2003-June/thread.html#553

Especially:

DLOG D40.  http://stderr.org/pipermail/inquiry/2003-May/000521.html
DLOG D71.  http://stderr.org/pipermail/inquiry/2003-June/000554.html

Take your pick, Gimli ...

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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