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33 lines
1.5 KiB
Markdown
33 lines
1.5 KiB
Markdown
---
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lastmod: "2021-09-12T22:47:44.0000000+01:00"
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author: patrick
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categories:
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- mathematical_summary
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comments: true
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date: "2016-04-21T00:00:00Z"
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aliases:
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- /modular-machines/
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title: Modular machines
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---
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I've written [a blurb][MM] about what a modular machine is (namely, another Turing-equivalent form of computing machine),
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and how a Turing machine may be simulated in one.
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(In fact, that blurb now contains an overview of how we may use modular machines to produce a group with insoluble word problem,
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and how to use them to embed a recursively presented group into a finitely presented one.)
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A modular machine is like a slightly more complicated version of a Turing machine, but it has the advantage
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that it is easier to embed a modular machine into a group than it is to embed a Turing machine directly into a group.
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We can use this embedding to show that there is a group with unsolvable word problem:
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solving the word problem would correspond to determining whether a certain Turing machine halted.
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This is as part of my revision process for the Part III course on "Infinite Groups and Decision Problems".
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It's probably more comprehensible if you already know what a modular machine is.
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Below are some notes which are handwritten, because I needed to draw pictures easily; the linked notes are typeset but might be less legible.
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![Notes1]
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![Notes2]
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[MM]: /misc/ModularMachines/EmbedMMIntoTuringMachine.pdf
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[Notes1]: /images/ModularMachines/ModularMachines1.jpg
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[Notes2]: /images/ModularMachines/ModularMachines2.jpg
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