Differential Analytic Turing Automata (DATA)

[Jon Awbrey]

SeqFans,

Speaking of computational complexity, which came up just recently,
the following resource may suggest some ideas to some people.

Differential Analytic Turing Automata
• https://oeis.org/wiki/Differential_Analytic_Turing_Automata_%E2%80%A2_Overview

The following example illustrates a span of ideas stretching through
the visions of Babbage, C.S. Peirce, Turing, and Cook.

Turing Machine Examples
• https://oeis.org/wiki/Differential_Analytic_Turing_Automata_%E2%80%A2_Part_2#Turing_Machine_Examples

Looking at what it takes to represent and perform a turing machine
computation in a propositional calculus formalism used as a purely
declarative programming language gives a sense of why propositional
calculus modeling is NP-complete.

The program I wrote through the 1980s which doesn't know anything
but how to index variables (in its sequential learning component)
and how to find models of formulas in propositional calculus (in
a differential extension of Peirce's graph-theoretic formalism)
was able to complete one bit of computation in a simulation of
the parity machine example, back in the day when I had only
640k of heap to play around with. But I designed the data
structures and algorithm in the sort of functional form
that promises of being vastly extensible. Folks with
a taste for retro computing or software archeology
may something to salvage there.

Theme One Program
• https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Overview

What remains to be done here is see how to convert instantaneous
state descriptions into differential transformations. That is
basically what mathematicians of former ages did to solve the
frame problem in physics and other dynamical systems.

I had begun developing some ideas along that line in
my work on differential logic.

Differential Logic and Dynamic Systems
• https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview

The wiki talk pages may be good places for further discussion
if anyone is tempted to do that ...

Regards,

Jon