From 1dc6d94fc245dc16e45baf3681c075d8353bc864 Mon Sep 17 00:00:00 2001 From: sejo Date: Wed, 8 Sep 2021 18:51:22 -0500 Subject: [PATCH] added cook link, and notes on turing completeness --- src/qiudanz_technique.gmo | 10 +++++++++- src/references.gmo | 4 +++- 2 files changed, 12 insertions(+), 2 deletions(-) diff --git a/src/qiudanz_technique.gmo b/src/qiudanz_technique.gmo index 7718630..633ae64 100644 --- a/src/qiudanz_technique.gmo +++ b/src/qiudanz_technique.gmo @@ -89,4 +89,12 @@ a way of complexifying any of these would be to learn to apply more than one tra another possibility would be to have beforehand a list of transformation to apply, with some or all of them being conditional on the movement currently in the head. -this would allow for turing-completeness :) +## turing completeness + +having some way of assigning the transformations to apply given the current movement in the head, would allow to perform arbitrary tag systems and/or turing machines, and m>1 tag systems are turing complete, e.g.: + +=> https://dspace.mit.edu/bitstream/1721.1/6107/2/AIM-052.pdf Universality of Tag Systems with P = 2 (1964) Cocke and Minsky + +however, cyclic tag systems are also turing complete, and they only require the sequential application of rules: + +=> https://wpmedia.wolfram.com/uploads/sites/13/2018/02/15-1-1.pdf Cook, Matthew (2004). "Universality in Elementary Cellular Automata" (PDF). Complex Systems. 15: 1–40. diff --git a/src/references.gmo b/src/references.gmo index 82fb8f0..ac260f0 100644 --- a/src/references.gmo +++ b/src/references.gmo @@ -41,7 +41,9 @@ texts by solderpunk in the {gemini} protocol => https://archive.org/details/computationfinit0000mins/ Computation: finite and infinite machines (1967) Minsky -=> https://www.semanticscholar.org/paper/Universality-of-Tag-Systems-with-P-%3D-2-Cocke-Minsky/ada3045434a410b4e84d2944590ff54fe5daa4ef Universality of Tag Systems with P = 2 (1964) Cocke and Minsky +=> https://dspace.mit.edu/bitstream/1721.1/6107/2/AIM-052.pdf Universality of Tag Systems with P = 2 (1964) Cocke and Minsky + +=> https://wpmedia.wolfram.com/uploads/sites/13/2018/02/15-1-1.pdf Cook, Matthew (2004). "Universality in Elementary Cellular Automata" (PDF). Complex Systems. 15: 1–40. # non-electronic computers