Differential Analytic Turing Automata

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Jon Awbrey

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Aug 1, 2020, 12:01:13 AM8/1/20
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Cf: Differential Analytic Turing Automata • Discussion 2
http://inquiryintoinquiry.com/2020/07/31/differential-analytic-turing-automata-%e2%80%a2-discussion-2/

Re: Scott Aaronson ( https://www.scottaaronson.com/ )
::: The Busy Beaver Frontier ( https://www.scottaaronson.com/blog/?p=4916 )

All,

Scott Aaronson's blog post and preprint about so-called
“Busy Beaver Functions” inspired me to go back and look
at some of the work I did in the late 1980s when I was
trying to understand Cook's Theorem in the theory of
computational complexity. A program I developed to
explore the integration of sequential learning and
propositional reasoning had a propositional calculus
module based on an extension of C.S. Peirce's logical
graphs, so I used that syntax to write out the clauses
for finite approximations to Turing machines, taking
the four-state parity machine from Herbert S. Wilf's
Algorithms and Complexity (1986) as an object example.
It was 1989 and all I had was a 289 PC with 600K heap,
but I was able to emulate a parity machine capable of
1 bit of computation. Here's a link to an exposition
of that.

• Differential Analytic Turing Automata
https://oeis.org/wiki/Differential_Analytic_Turing_Automata_%E2%80%A2_Overview
• Part 1
https://oeis.org/wiki/Differential_Analytic_Turing_Automata_%E2%80%A2_Part_1
• Part 2
https://oeis.org/wiki/Differential_Analytic_Turing_Automata_%E2%80%A2_Part_2

It may be quicker to skip to Part 2 and refer to Part 1 only as needed.

I'll work up the case of a 2-state Busy Beaver when I get a chance.
I always learned a lot just from looking at the propositional form.

Regards,

Jon

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