File:Kolmogorov complexity and computable lower bounds pdf.pdf
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[edit]DescriptionKolmogorov complexity and computable lower bounds pdf.pdf |
English: Shows the Kolmogorov complexity K(s) (red), and two computable lower bound functions, prog1(s) (green), prog2(s) (blue). The horizontal axis (logarithmic scale) enumerates all strings s, ordered by length; the vertical axis (linear scale) measures string length in bits; the depth axis lines up the shown functions. Most strings are incompressible, i.e. their Kolmogorov complexity exceeds their length by a constant amount. Nine compressible strings are shown in the picture, appearing as almost vertical slopes. Due to Chaitin's incompleteness theorem, the output of any program computing a lower bound of the Kolmogorov complexity cannot exceed some fixed limit, which is independent of the input string s; hence both the blue and the green line eventually turn horizontal. |
Date | |
Source | Own work |
Author | Jochen Burghardt |
Other versions |
LaTeX source code |
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\documentclass[12pt]{article}
\setlength{\unitlength}{1mm}
\usepackage[pdftex]{color}
\usepackage{amssymb}
\usepackage[paperwidth=210mm,paperheight=55mm]{geometry}
\setlength{\topmargin}{-36mm}
\setlength{\textwidth}{210mm}
\setlength{\textheight}{55mm}
\setlength{\oddsidemargin}{-23mm}
\setlength{\parindent}{0cm}
\pagestyle{empty}
% colors
\definecolor{cCmpr} {rgb}{0.80,0.80,0.80} % compressible string
\definecolor{cClr} {rgb}{1.00,1.00,1.00} % white background
\definecolor{cI} {rgb}{0.00,0.80,0.00} % lwb prog 1
\definecolor{cJ} {rgb}{0.00,0.00,0.99} % lwb prog 2
\definecolor{cKolm} {rgb}{0.99,0.00,0.00} % kolm compl
%\definecolor{cBg} {rgb}{0.00,0.80,0.80} % background
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\newcommand{\cmdKolm}{%
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|
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 16:19, 4 March 2020 | ![]() | 1,239 × 322 (37 KB) | Jochen Burghardt (talk | contribs) | decreased length of axes |
22:56, 3 March 2020 | No thumbnail | 0 × 0 (38 KB) | Jochen Burghardt (talk | contribs) | User created page with UploadWizard |
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Conversion program | pdfTeX-1.40.18 |
Encrypted | no |
Page size | 595.276 x 155.905 pts |
Version of PDF format | 1.5 |