50 lines
No EOL
12 KiB
HTML
50 lines
No EOL
12 KiB
HTML
<!DOCTYPE html><html><head><meta content="text/html; charset=utf-8" http-equiv="Content-Type" /><meta content="width=device-width, initial-scale=1" name="viewport" /><!--replace-start-0--><!--replace-start-5--><!--replace-start-8--><title>Turing Completeness - My Zettelkasten</title><!--replace-end-8--><!--replace-end-5--><!--replace-end-0--><link href="https://cdn.jsdelivr.net/npm/fomantic-ui@2.8.7/dist/semantic.min.css" rel="stylesheet" /><link href="https://fonts.googleapis.com/css?family=Merriweather|Libre+Franklin|Roboto+Mono&display=swap" rel="stylesheet" /><!--replace-start-1--><!--replace-start-4--><!--replace-start-7--><link href="https://raw.githubusercontent.com/srid/neuron/master/assets/neuron.svg" rel="icon" /><meta content="We know that a Turing machine is a theoretical construct of a computer that:" name="description" /><meta content="Turing Completeness" property="og:title" /><meta content="My Zettelkasten" property="og:site_name" /><meta content="article" property="og:type" /><meta content="Turing_completeness" property="neuron:zettel-id" /><meta content="Turing_completeness" property="neuron:zettel-slug" /><meta content="Turing" property="neuron:zettel-tag" /><meta content="theory-of-computation" property="neuron:zettel-tag" /><script type="application/ld+json">[]</script><style type="text/css">body{background-color:#eeeeee !important;font-family:"Libre Franklin", serif !important}body .ui.container{font-family:"Libre Franklin", serif !important}body h1, h2, h3, h4, h5, h6, .ui.header, .headerFont{font-family:"Merriweather", sans-serif !important}body code, pre, tt, .monoFont{font-family:"Roboto Mono","SFMono-Regular","Menlo","Monaco","Consolas","Liberation Mono","Courier New", monospace !important}body div.z-index p.info{color:#808080}body div.z-index ul{list-style-type:square;padding-left:1.5em}body div.z-index .uplinks{margin-left:0.29999em}body .zettel-content h1#title-h1{background-color:rgba(33,133,208,0.1)}body nav.bottomPane{background-color:rgba(33,133,208,2.0e-2)}body div#footnotes{border-top-color:#2185d0}body p{line-height:150%}body img{max-width:100%}body .deemphasized{font-size:0.94999em}body .deemphasized:hover{opacity:1}body .deemphasized:not(:hover){opacity:0.69999}body .deemphasized:not(:hover) a{color:#808080 !important}body div.container.universe{padding-top:1em}body div.zettel-view ul{padding-left:1.5em;list-style-type:square}body div.zettel-view .pandoc .highlight{background-color:#ffff00}body div.zettel-view .pandoc .ui.disabled.fitted.checkbox{margin-right:0.29999em;vertical-align:middle}body div.zettel-view .zettel-content .metadata{margin-top:1em}body div.zettel-view .zettel-content .metadata div.date{text-align:center;color:#808080}body div.zettel-view .zettel-content h1{padding-top:0.2em;padding-bottom:0.2em;text-align:center}body div.zettel-view .zettel-content h2{border-bottom:solid 1px #4682b4;margin-bottom:0.5em}body div.zettel-view .zettel-content h3{margin:0px 0px 0.4em 0px}body div.zettel-view .zettel-content h4{opacity:0.8}body div.zettel-view .zettel-content div#footnotes{margin-top:4em;border-top-style:groove;border-top-width:2px;font-size:0.9em}body div.zettel-view .zettel-content div#footnotes ol > li > p:only-of-type{display:inline;margin-right:0.5em}body div.zettel-view .zettel-content aside.footnote-inline{width:30%;padding-left:15px;margin-left:15px;float:right;background-color:#d3d3d3}body div.zettel-view .zettel-content .overflows{overflow:auto}body div.zettel-view .zettel-content code{margin:auto auto auto auto;font-size:100%}body div.zettel-view .zettel-content p code, li code, ol code{padding:0.2em 0.2em 0.2em 0.2em;background-color:#f5f2f0}body div.zettel-view .zettel-content pre{overflow:auto}body div.zettel-view .zettel-content dl dt{font-weight:bold}body div.zettel-view .zettel-content blockquote{background-color:#f9f9f9;border-left:solid 10px #cccccc;margin:1.5em 0px 1.5em 0px;padding:0.5em 10px 0.5em 10px}body div.zettel-view .zettel-content.raw{background-color:#dddddd}body .ui.label.zettel-tag{color:#000000}body .ui.label.zettel-tag a{color:#000000}body nav.bottomPane ul.backlinks > li{padding-bottom:0.4em;list-style-type:disc}body nav.bottomPane ul.context-list > li{list-style-type:lower-roman}body .footer-version img{-webkit-filter:grayscale(100%);-moz-filter:grayscale(100%);-ms-filter:grayscale(100%);-o-filter:grayscale(100%);filter:grayscale(100%)}body .footer-version img:hover{-webkit-filter:grayscale(0%);-moz-filter:grayscale(0%);-ms-filter:grayscale(0%);-o-filter:grayscale(0%);filter:grayscale(0%)}body .footer-version, .footer-version a, .footer-version a:visited{color:#808080}body .footer-version a{font-weight:bold}body .footer-version{margin-top:1em !important;font-size:0.69999em}@media only screen and (max-width: 768px){body div#zettel-container{margin-left:0.4em !important;margin-right:0.4em !important}}body span.zettel-link-container span.zettel-link a{color:#2185d0;font-weight:bold;text-decoration:none}body span.zettel-link-container span.zettel-link a:hover{background-color:rgba(33,133,208,0.1)}body span.zettel-link-container span.extra{color:auto}body span.zettel-link-container.errors{border:solid 1px #ff0000}body span.zettel-link-container.errors span.zettel-link a:hover{text-decoration:none !important;cursor:not-allowed}body [data-tooltip]:after{font-size:0.69999em}body div.tag-tree div.node{font-weight:bold}body div.tag-tree div.node a.inactive{color:#555555}body .tree.flipped{-webkit-transform:rotate(180deg);-moz-transform:rotate(180deg);-ms-transform:rotate(180deg);-o-transform:rotate(180deg);transform:rotate(180deg)}body .tree{overflow:auto}body .tree ul.root{padding-top:0px;margin-top:0px}body .tree ul{position:relative;padding:1em 0px 0px 0px;white-space:nowrap;margin:0px auto 0px auto;text-align:center}body .tree ul::after{content:"";display:table;clear:both}body .tree ul:last-child{padding-bottom:0.1em}body .tree li{display:inline-block;vertical-align:top;text-align:center;list-style-type:none;position:relative;padding:1em 0.5em 0em 0.5em}body .tree li::before{content:"";position:absolute;top:0px;right:50%;border-top:solid 2px #cccccc;width:50%;height:1.19999em}body .tree li::after{content:"";position:absolute;top:0px;right:50%;border-top:solid 2px #cccccc;width:50%;height:1.19999em}body .tree li::after{right:auto;left:50%;border-left:solid 2px #cccccc}body .tree li:only-child{padding-top:0em}body .tree li:only-child::after{display:none}body .tree li:only-child::before{display:none}body .tree li:first-child::before{border-style:none;border-width:0px}body .tree li:first-child::after{border-radius:5px 0px 0px 0px}body .tree li:last-child::after{border-style:none;border-width:0px}body .tree li:last-child::before{border-right:solid 2px #cccccc;border-radius:0px 5px 0px 0px}body .tree ul ul::before{content:"";position:absolute;top:0px;left:50%;border-left:solid 2px #cccccc;width:0px;height:1.19999em}body .tree li div.forest-link{border:solid 2px #cccccc;padding:0.2em 0.29999em 0.2em 0.29999em;text-decoration:none;display:inline-block;border-radius:5px 5px 5px 5px;color:#333333;position:relative;top:2px}body .tree.flipped li div.forest-link{-webkit-transform:rotate(180deg);-moz-transform:rotate(180deg);-ms-transform:rotate(180deg);-o-transform:rotate(180deg);transform:rotate(180deg)}</style><script
|
||
async=""
|
||
id="MathJax-script"
|
||
src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"
|
||
></script>
|
||
<link
|
||
href="https://cdnjs.cloudflare.com/ajax/libs/prism/1.23.0/themes/prism.min.css"
|
||
rel="stylesheet"
|
||
/><link rel="preconnect" href="https://fonts.googleapis.com" /><link
|
||
rel="preconnect"
|
||
href="https://fonts.gstatic.com"
|
||
crossorigin
|
||
/><link
|
||
href="https://fonts.googleapis.com/css2?family=IBM+Plex+Mono:ital,wght@0,100;0,200;0,300;0,400;0,500;0,600;0,700;1,100;1,200;1,300;1,400;1,500;1,600;1,700&family=IBM+Plex+Sans+Condensed:ital,wght@0,100;0,200;0,300;0,400;0,500;0,600;0,700;1,100;1,200;1,300;1,400;1,500;1,600;1,700&family=IBM+Plex+Sans:ital,wght@0,100;0,200;0,300;0,400;0,500;0,600;0,700;1,100;1,200;1,300;1,400;1,500;1,600;1,700&family=IBM+Plex+Serif:ital,wght@0,100;0,200;0,300;0,400;0,500;0,600;0,700;1,100;1,200;1,300;1,400;1,500;1,600;1,700&display=swap"
|
||
rel="stylesheet"
|
||
/>
|
||
<script src="https://cdnjs.cloudflare.com/ajax/libs/prism/1.23.0/components/prism-core.min.js"></script>
|
||
<script src="https://cdnjs.cloudflare.com/ajax/libs/prism/1.23.0/plugins/autoloader/prism-autoloader.min.js"></script>
|
||
<style>
|
||
body .ui.container,
|
||
body ul {
|
||
font-family: "IBM Plex Sans" !important;
|
||
}
|
||
body blockquote {
|
||
border-left-width: 3px !important;
|
||
font-style: italic;
|
||
}
|
||
.headerFont,
|
||
.ui.header,
|
||
body h1,
|
||
h2,
|
||
h3,
|
||
h4,
|
||
h5,
|
||
h6 {
|
||
font-family: "IBM Plex Sans Condensed" !important;
|
||
}
|
||
body p {
|
||
line-height: 1.4;
|
||
}
|
||
.monoFont,
|
||
body code,
|
||
pre,
|
||
tt {
|
||
font-family: "IBM Plex Mono" !important;
|
||
font-size: 12px !important;
|
||
line-height: 1.4 !important;
|
||
}
|
||
</style>
|
||
<!--replace-end-7--><!--replace-end-4--><!--replace-end-1--></head><body><div class="ui fluid container universe"><!--replace-start-2--><!--replace-start-3--><!--replace-start-6--><div class="ui text container" id="zettel-container" style="position: relative"><div class="zettel-view"><article class="ui raised attached segment zettel-content"><div class="pandoc"><h1 id="title-h1">Turing Completeness</h1><p>We know that a <span class="zettel-link-container cf"><span class="zettel-link" title="Zettel: Turing Machines"><a href="Turing_machines.html">Turing machine</a></span></span> is a theoretical construct of a computer that:</p><blockquote><p>contains mutable state, executes sequences of simple instructions that read and write that state, and can pick different execution paths depending on the state (via conditional branch instructions.)</p></blockquote><p>A Turing Complete (TC) system is a system that abides by, or can be reduced to, the above description.</p><p>TC also serves as a <em>definition of computability</em> and provides a formal basis for conceiving of computation at a theoretical level.</p><p>All Turing Complete systems are functionally equivalent. This means they can simulate each other given enough time and memory. Similarly a TC system can in principle perform any computation that any other programmable computer can perform. This is true for <em>other</em> TC systems and also those that are not TC however the inverse doesn’t hold: a non-TC system cannot emulate a TS system. For instance a calculator cannot do what a TC smart phone can do. But a smart phone can act as a calculator.</p><p>This concept of completeness is also expressed in terms of a Universal Turing Machine - a TM capable of simulating any other Turing machine. Given that the ability of a TM to simulate another TM is the condition for completeness, a TC system is also a UTM.</p><p>Completeness applies to the hardware of computers as well as their software.</p><p>Turing Completeness is the theoretical basis of the practical concept of a “general-purpose computer”: a general-purpose computer is such because it is TC - it can in theory compute anything that is computable.</p><p>Most modern programming languages are Turing Complete in that they can, in theory, be used to compute anything that is computable.</p></div></article><nav class="ui attached segment deemphasized bottomPane" id="neuron-tags-pane"><div><span class="ui basic label zettel-tag" title="Tag">Turing</span><span class="ui basic label zettel-tag" title="Tag">theory-of-computation</span></div></nav><nav class="ui bottom attached icon compact inverted menu blue" id="neuron-nav-bar"><!--replace-start-9--><!--replace-end-9--><a class="right item" href="impulse.html" title="Open Impulse"><i class="wave square icon"></i></a></nav></div></div><!--replace-end-6--><!--replace-end-3--><!--replace-end-2--><div class="ui center aligned container footer-version"><div class="ui tiny image"><a href="https://neuron.zettel.page"><img alt="logo" src="https://raw.githubusercontent.com/srid/neuron/master/assets/neuron.svg" title="Generated by Neuron 1.9.35.3" /></a></div></div></div></body></html> |