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 inquiry into inquiry: https://inquiryintoinquiry.com/ academia: https://independent.academia.edu/JonAwbrey oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey facebook page: https://www.facebook.com/JonnyCache
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